Russian and Ukrainian negotiators met on Thursday and Kyiv said it would call for a ceasefire and humanitarian corridors to evacuate its besieged citizens, as the war entered its second week.
Hundreds of Russian soldiers and Ukrainian civilians have been killed since President Vladimir Putin sent his troops over the border on February 24.
Russia itself has been plunged into isolation never before experienced by an economy of such size.
The United Nations said more than 1 million refugees had fled in just seven days, one of the fastest exoduses in memory.
Ukrainian negotiator and presidential adviser Mikhailo Podolyak tweeted a picture of the delegations at a conference table in an undisclosed location.
The Ukrainians wore battle fatigues and winter jackets; the Russians wore suits and ties.
Podolyak said Ukraine would demand an immediate ceasefire, armistice and "humanitarian corridors for the evacuation of civilians from destroyed or constantly shelled villages/cities."
Neither side has suggested it was expecting breakthroughs after a first round of talks held in Belarus on Monday led to no progress.
Despite an initial battle plan that Western countries said was aimed at swiftly toppling the Kyiv government it describes as dangerous nationalists who threaten its security, Russia has captured only one Ukrainian city so far - the southern Dnipro River port of Kherson, which its tanks entered on Wednesday.
With its main assault force halted for days on a highway north of Kyiv, Russia has shifted tactics, escalating its bombardment of major cities.
Swathes of central Kharkiv, a city of 1.5 million people, have been blasted into rubble.
Mariupol, the main port of eastern Ukraine, has been surrounded under heavy bombardment, with no water or power.
Officials say they cannot evacuate the wounded.
The city council compared the situation to the World War Two siege of Leningrad.
Ukraine's President Volodymyr Zelenskiy has stayed in Kyiv, releasing regular video updates to the nation.
In his latest message, he said Ukrainian lines were holding. "We have nothing to lose but our own freedom," he said.
Britain's defence ministry said the main body of the huge Russian column advancing on Kyiv was still 30 km (19 miles) from the city centre, held up by Ukrainian resistance, mechanical breakdown and congestion.
In Borodyanka, a small town 60 km (40 miles) northwest of Kyiv where locals had repelled a Russian assault, burnt out hulks of destroyed Russian armour were scattered on a highway, surrounded by buildings blasted into ruins.
Flames from one burning apartment building lit up the pre-dawn sky.
At least nine people were killed and four wounded in a Russian air strike that hit two schools and private houses in the eastern Chernihiv region on Thursday, governor Viacheslav Chaus said in an online post.
Amid Moscow's increasing diplomatic isolation, only Belarus, Eritrea, Syria and North Korea voted with Russia against an emergency resolution at the United Nations General Assembly condemning Moscow's "aggression".
Putin spoke by telephone to French President Emmanuel Macron on Thursday, telling him Russia would achieve its goals, including the demilitarisation and neutrality of Ukraine, the Kremlin said.
The International Criminal Court's top prosecutor said an advance team had left The Hague for the Ukraine region on Thursday to start investigating possible war crimes.