Any compromises agreed with Russia to end its invasion will need to be voted on in a referendum, Ukrainian President Volodymyr Zelenskyy has said.
Issues of concern could include security guarantees offered in lieu of NATO membership, and areas occupied by Russian forces, such as Crimea.
Ukrainian citizens will "have to speak up and respond to this or that form of compromise", Mr Zelenskyy said.
Potential compromises "will be the subject of our talks and understanding between Ukraine and Russia", he said in comments published by Ukrainian public broadcaster Suspilne.
Other key developments:
• Ukraine has refused to give up the besieged city of Mariupol despite Russia's demands to surrender
• Another curfew lasting 40 hours from Monday night has been announced in the capital Kyiv
• Kremlin says more progress needed in peace talks before Putin and Zelenskyy can meet face-to-face
• Ukraine's nuclear regulatory agency says the radiation monitors around the Chernobyl have stopped working
• Russia has claimed it targeted a shopping centre in Kyiv because it was being used to store rockets
Ukraine war live updates: Russia-US relations 'on brink of collapse'
Ukrainian service members inspect a shell crater in east Kyiv
'No talk of any surrender' across Ukraine's major cities
Russia has continued to bombard the devastated Mariupol and intensified its attacks on Kyiv, while also targeting another port city – Odesa – for the first time.
But Ukraine's deputy prime minister said there would be "no talk of any surrender" or of "laying down of arms".
Residents refused Moscow's offer of "safe passage" out of Mariupol after a deadline of 5am was set.
In Kyiv, Mayor Vitali Klitschko announced a 40-hour curfew. It began at 8pm local time on Monday night and runs until 7am on Wednesday, as the city faces "more shelling".
Elsewhere, Ukrainian forces are also holding on to the eastern city of Kharkiv after five civilians died in Russian shelling on Saturday – including a nine-year-old boy, said regional police.
Sky correspondent John Sparks travelled with the Ukrainian military to the front line on the outskirts of the city and described the "air filled with the deep-sounding boom of tank and artillery fire".
The Russian advance on Kyiv appears to be in trouble, according to the UK's Ministry of Defence.
It says Vladimir Putin's forces advancing from the northeast have stalled – and the bulk remain more than 15 miles (25km) from the centre of the capital.
But Kyiv remains "Russia's primary military objective" and it is "likely to prioritise attempting to encircle the city over the coming weeks".
Russia accused of 'committing genocide'
Ukraine's defence minister, Oleksii Reznikov, has accused Moscow of "committing a real act of genocide" and said Russian forces had killed more than 150 children, destroyed more than 400 schools and nurseries and 110 hospitals.
He reiterated calls for NATO to establish a no-fly zone over Ukraine and demanded tougher sanctions against the Kremlin to "stop the evil" and "state terrorism".
At least eight people have been killed by Russian shelling in the capital, with a shopping centre, residential buildings offices and a gym among the places hit in the Podil district, police said.
"We saw a number of bodies laid out on the pavement outside the mall," said Sky's Alex Crawford.
One woman told her: "We heard a really loud explosion. We were in our apartment nearby and there was a terrible, big noise. We don't feel safe anywhere in Ukraine right now."
But shortly afterwards, photographs began circulating on the internet which appeared to show the shopping mall with military vehicles parked underneath. It is not clear how recent these photographs are or their origin.
Read more: Russia attacked Kyiv shopping centre 'because it was being used to store rockets'
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Massive explosion hits Kyiv shopping centre
First Russian assault on Odesa
Authorities in Odesa accused Russian forces of targeting civilians after a strike on homes in the city outskirts – the first such attack on the Black Sea port city.
"These are residential buildings where peaceful people live," mayor Gennadiy Trukhanov was quoted as saying.
"We will not leave Odesa, and we will fight for our city."
The city council said there were no casualties, although the shelling caused a fire.
In the early hours, residents heard "large bangs" coming from the Black Sea, where there has been a Russian naval build-up for the past week, said Sky correspondent Nick Martin.
Shrapnel from the shelling peppered holes into buildings, including flats, and smashed windows – sending shards of glass cascading down on to the streets of the city and so-called jewel of the Black Sea.
Homes damaged by shelling in Odesa, Ukraine. Pic: AP
A man clears a broken window in the aftermath of a military strike in Odesa, Ukraine
Russia docks landing support ship near Mariupol
Russia says it has docked a large, landing support ship, the Orsk, in the occupied Ukrainian port of Berdyansk, 45 miles (70km) southwest of Mariupol on the Sea of Azov.
"It is hard to overestimate the possibilities of using this port," said the website of the Russian armed forces news outlet Zvezda (Star). "Now the southern flank of the special operation can receive everything necessary at any time, including equipment and ammunition."
The website said 10 such ships – each can carry up to 20 tanks or 40 armoured personnel carriers – are part of what Moscow has called its "special military invasion" in Ukraine.
Mariupol, which sits between Russian military bases in Crimea and the disputed Donbas region in eastern Ukraine, has been surrounded from the outset of the invasion because its capture would allow Russian forces to unite.
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Destroyed Mariupol seen from above
Siege of Mariupol 'a terror that will be remembered for centuries'
Speaking earlier on Monday, Ukrainian President Volodymyr Zelenskyy said: "They are under the rubble, and we don't know how many survived.
"But we know that we will certainly shoot down the pilot who dropped that bomb, like about 100 such mass murderers whom we already have downed."
He has described the siege of Mariupol a war crime and "a terror that will be remembered for centuries to come".
Ukraine has accused Russian forces of bombarding buildings including a maternity hospital, swimming pool and a shopping centre – as well as a theatre where it said people were sheltering last week.
Hundreds of men, women, and children were thought to have been in the theatre's basement after their homes were destroyed during the invasion – and the word "children" had been displayed in large letters at the site.
The city's authorities have said at least 2,300 people have died, some buried in mass graves.
Read more: How the last journalists to leave Mariupol escaped with their lives
Signs war headed for 'stalemate rather than negotiated solution'
The war is headed for "a long, grinding campaign" where the Russians "try and smash one town after another in the hope of breaking the will of the Ukrainian people", former Foreign Office permanent secretary and national security adviser Lord Ricketts has said.
He told Sky News: "I think it is clear the Russians cannot win an outright victory – the Ukrainian resistance has been far too strong for that. We have seen even in Mariupol, after weeks and weeks of smashing that city to pieces, people are not ready to surrender to Russian forces.
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"How much more difficult will that be in a massive city like Kyiv? They are clearly stalled, bogged down, all kinds of problems with their logistics and I don't think they are ready yet to declare any kind of a ceasefire negotiation. The positions of the two sides are far too far apart for that.
"I think we are in for a stalemate rather than a negotiated solution."
Ten million people have been displaced by the conflict, including nearly 3.5 million who have fled abroad, according to the UN refugee agency.
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