Russian forces are closing in on Kyiv in a 17-mile convoy of hundreds of tanks and other vehicles, with loud large explosions heard in the Ukrainian capital, after the first round of peace talks ended with no immediate agreement.
Sky's security and defence editor Deborah Haynes said "the windows rattled with those explosions we heard" in the Ukrainian capital.
"The warning has always been that if they couldn't have their success in their initial wave then they would up the tempo in terms of the level of violence which seems to be what we are seeing and hearing."
Ukraine-Russia news live: Peace talks end with more expected in coming days
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'Help us or war will come knocking'
'Help us or war will come knocking'
Russian troops are attacking on multiple fronts and are believed to be around 25km (15 miles) from Kyiv.
Satellite imagery from the Maxar company shows a huge convoy of hundreds of armoured vehicles, tanks, artillery and support vehicles has been spotted near the capital.
The images also captured signs of fighting outside Kyiv, including destroyed vehicles and a damaged bridge.
Messages aimed at the advancing Russian soldiers popped up on billboards, bus stops and electronic traffic signs across Kyiv.
"Russian soldier – Stop! Remember your family. Go home with a clean conscience," one read.
Read more: Russia's invasion of Ukraine mapped – what happened on day five
And Ukraine's defence minister has offered amnesty and money to any Russian soldiers who lay down their weapons.
Oleksii Reznikov posted on social media: "Those of you who do not want to become a murderer and die can save yourselves."
Earlier, the Ukrainian interior ministry said dozens of people had been killed in mass shelling in Kharkiv, as fierce fighting continues into the fifth day of the conflict.
"Kharkiv has just been massively fired upon by grads (rockets). Dozens of dead and hundreds of wounded," Ukrainian interior ministry adviser Anton Herashchenko said in a post on Facebook.
Deborah Haynes added: "There has been a horrific bombardment of Ukraine's second city. The images that are appearing… give a sense that something very horrific has happened."
Ukrainian President Volodymr Zelenskyy has said it is time to consider a no-fly zone for Russian missile, planes and helicopters in response to the shelling of Kharkiv.
In a video address, Mr Zelenskyy did not specify how and by whom a no-fly zone would be enforced.
He said Russia had launched 56 rocket strikes and fired 113 cruise missiles against Ukraine in the past five days.
Oksana Markarova, the Ukrainian ambassador to the US, told Congress that Russia used a vacuum bomb on Monday.
She said: "They used the vacuum bomb today, which is actually prohibited by the Geneva convention.
"The devastation that Russia is trying to inflict on Ukraine is large."
A vacuum bomb, sometimes referred to as a thermobaric weapon or aerosol bomb, is a type of explosive that uses oxygen from the surrounding air to generate a high-temperature explosion.
Western officials are concerned there will be significant civilian casualties as there is also evidence of weapons being used in an indiscriminate nature in cities.
They added the next 48 hours will be key to whether Russia can achieve its original objective of encircling Kyiv.
And they are certain Moscow miscalculated the response of countries around the world and the show of unity throughout Europe.
Meanwhile, Brazil's far-right populist leader Jair Bolsonaro, who has refused to condemn Russian President Vladimir Putin while remaining neutral over the invasion, has said Ukrainians may be able to come to his country on a humanitarian visa.
In an interview with TV channel Jovem Pan, Mr Bolsonaro said the country will do whatever is possible to receive Ukrainians in Brazil.
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On Monday afternoon, Mr Zelenskyy said he had signed an official request for Ukraine to join the European Union.
He has asked the EU to allow Ukraine to gain membership immediately under a special procedure as it defends itself from invasion by Russian forces.
Mr Zelenskyy also signed a decree temporarily lifting the requirement for entry visas for any foreigner willing to join Ukraine's International Defence Legion and fight on Ukraine's side against invading Russian troops.
The decree takes effect from Tuesday and will remain in effect as long as martial law is in place.
It comes as the office of the prosecutor of the International Criminal Court said it will seek approval to open an investigation into alleged war crimes in Ukraine.
"The next step is to proceed with the process of seeking and obtaining authorisation from the Pre-Trial Chamber of the Court to open an investigation," the prosecutor said in a statement on Monday.
Analysis: Dominic Waghorn, international affairs editor
For talks to be happening is a sign of progress. Less encouraging is the backdrop in Ukraine, especially Kharkiv which has come under sustained shelling or rocket fire by Russian forces.
The two countries had wrangled all weekend over the venue of talks, Ukraine preferring Warsaw, Russia Minsk.
They settled on a compromise, the Belarussian town of Gomel near the Belarus Ukraine border. They had set conditions for the talks.
Russia demanding the demilitarisation of Ukraine, Ukraine Russia cease hostilities. The US government had cautioned Ukraine not to negotiate at the barrel of a gun, but the two sides agreed to talk anyway.
Ukraine used its opening session to demand Russia remove its forces from all of Ukraine, included Crimea, annexed by Russia in 2014 and the Donbass where Russia has confected a civil war since the same year.
Is Russia genuine about talks and piling on the pressure militarily to increase its leverage or using diplomacy as a gambit to play for time while it can build up forces to renew its offensive in Ukraine in earnest? Too early to say.
Meanwhile, Ukraine officials said the first round of talks with Russia about ending the fighting had concluded and that more talks could happen soon.
"The Russian side, unfortunately, still has a very biased view of the destructive processes it has launched," Ukrainian
presidential adviser Mykhailo Podolyak said on Twitter after attending the talks near the Belarusian border.
It comes after Mr Putin put Russia's nuclear deterrent on high alert in the face of a barrage of Western-led reprisals for his invasion of Ukraine.
He called the West an "empire of lies" on Monday, as he discussed the economic and financial impact of sweeping sanctions against Moscow with his top officials.
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UK Defence Secretary Ben Wallace described Mr Putin's comments as "a big attempt to distract away from his troubles in Ukraine" by reminding the world Russia has nuclear capability.
The Kremlin said the supply of weapons to Ukraine by its allies in the West is "dangerous and destabilising", but did not comment on Mr Putin's orders.
It also made the unfounded claim that Ukrainian forces are using civilians as human shields – which was dismissed by Danylo Lubkivskyi, a Ukrainian diplomat and former deputy foreign minister, as a "lie" and Russian "propaganda".
UK Prime Minister Boris Johnson spoke to Mr Zelenskyy on Monday afternoon, committing to send more military support "in the coming hours and days".
Mr Johnson also said the UK will "continue to bring maximum pressure to bear" on Russia as he pledged that Mr Putin would "feel the consequences" for invading Ukraine.
On the eve of his trip on Tuesday to Poland and Estonia, Boris Johnson said international leaders were united in agreeing that the Russian president "must fail" after his decision to send troops into the neighbouring country.
Mr Johnson is due to meet with Warsaw and Tallinn leaders and visit British troops serving in Estonia, which shares a border with Russia.
Ukrainian forces have so far appeared to slow the invasion by Russian Armed Forces, with the UK Ministry of Defence saying in an update "logistical failures and staunch Ukrainian resistance continue to frustrate the Russian advance" and that for the first time in the conflict Russia has been "forced to acknowledge suffering casualties".
Heavy fighting continues around Kharkiv – Ukraine's second largest city – and Chernihiv, but both cities remain under Ukrainian control.
'Russian saboteurs' shoot dead girl and her parents in family car
There are conflicting numbers on civilian deaths – the UN estimates at least 102 citizens have died, including seven children, while it says more than half a million refugees have fled Ukraine.
Ukraine's health ministry said on Sunday that 352 civilians, including 14 children, had been killed since the beginning of Russia's invasion of Ukraine. It also said that 1,684 people, including 116 children, had been wounded.
The first fatality to be named is a girl from Kyiv called Polina, who was in her final year of primary school.
She and her parents were shot dead by a Russian sabotage and reconnaissance group who opened fire on the family car, the city's deputy mayor Volodymyr Bondarenko said in a Facebook post.
'Bombs dropping in Kyiv'
A UK expat who fled the country with his family and is now in Poland said they could hear "bombs dropping in Kyiv" as they left.
Stuart McKenzie told Sky News he initially wanted to stay and "support Ukraine" but decided with his wife that "if there was any danger to our children – that is the point we would have to leave the city".
Six-year-old girl 'killed by shelling' in Mariupol
In the port city of Mariupol a six-year-old girl who was injured during shelling died in hospital.
Her bloodied pyjamas were decorated with cartoon unicorns, according to the Associated Press news agency, which quoted a hospital worker shouting, "Take her out! Take her out! We can make it!", as she arrived in an ambulance.
The doctor who tried to save her reportedly told the AP journalist allowed inside: "Show this to Putin."
The United Nations has said that more than 500,000 people have fled Ukraine to neighbouring countries since the start of Russia's invasion.