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 one million refugees had fled in just seven days, one of the fastest exoduses in memory.
Ukrainian negotiator Davyd Arakhamia posted a picture on Facebook of himself preparing to board a helicopter for talks.
"The minimum program: humanitarian corridors," he said.
"We have started talking to Russia's representatives," adviser Mykhailo Podolyak said on Twitter.
The Russian delegation is led by presidential adviser Vladimir Medinsky, while the Ukrainian delegation is led by Arakhamia, the head of President Volodymyr Zelenskiy's ruling party.
While the Russian representatives wore suits, the Ukrainians were clad in olive-green military jumpers.
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 the US and its allies says 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 II siege of Leningrad.
Zelenskiy has stayed in Kyiv, releasing regular video updates.
In his latest message, he said Ukrainian lines were holding.
"We have nothing to lose but our own freedom," he said.
In Borodyanka, a small town 60km 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.
"They started shooting from their APC towards the park in front of the post office," a man recounted in the apartment where he was sheltering with his family, referring to a Russian armoured personnel carrier.
"Then those bastards started the tank and started shooting into the supermarket which was already burned. It caught fire again.
"An old man ran outside like crazy, with big round eyes, and said 'give me a Molotov cocktail! I just set their APC on fire!...Give me some petrol, we'll make a Molotov cocktail and burn the tank!'."
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.
Two cargo ships came under apparent attack at Ukrainian ports.
Four crew members were missing after Estonian-owned ship exploded and sank off Odessa, and at least one crew member was killed in a blast on a Bangladeshi ship at Olvia.
Ukraine is one of the world's biggest grain and food oil exporters from its Black Sea ports.
Amid Russia'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 its "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.
Macron told Putin "you are lying to yourself" about the government in Kyiv, and said the war would cost Russia dearly, a French official said.
with reporting from DPA
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