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The agreement was the only real progress from a second round of talks between Moscow and Kyiv, an adviser to Ukraine's President Volodymyr Zelenskyy said, and it was not immediately clear how they would work.
A Russian negotiator, nationalist politician Leonid Slutsky, said the corridors would be introduced soon.
The two sides met after the fall of the first major Ukrainian city to Russian forces, with Mr Putin apparently unwilling to heed a global demand for hostilities to end as the war entered its second week.
He again said Russia was rooting out "neo-Nazis", adding during the televised opening of a national security council meeting that he "will never give up on (his) conviction that Russians and Ukrainians are one people".
Mr Zelenskyy has called on the West to increase its military assistance, after Nato members ruled out enforcing a no-fly zone for fear of igniting a direct war with nuclear-armed Russia.
"If you do not have the power to close the skies, then give me planes," Mr Zelenskyy said.
"If we are no more then, God forbid, Latvia, Lithuania, Estonia will be next."
He said that direct talks with Mr Putin were "the only way to stop this war".
The EU has already offered fighter jets, and a source in Berlin said the German government was planning to deliver another 2,700 anti-aircraft missiles to Ukraine.
The 27-nation bloc agreed to approve temporary protection for all refugees fleeing the war in Ukraine. The UN says more than one million people have already fled the country.
At the talks on the Belarus-Poland border, both sides shook hands across a table at the outset, with the Ukrainian delegates in military attire and the Russians in more formal suits.
A first round of talks on Monday also yielded no breakthrough, and Kyiv says it will not accept any Russian "ultimatums".
The invasion, now in its eighth day, has turned Russia into a global pariah in the worlds of finance, diplomacy, sports and culture.
The UN has opened a probe into alleged war crimes, as the Russian military bombards cities in Ukraine with shells and missiles, forcing civilians to cower in basements.
Addressing the Mr Putin regime in a video, Mr Zelenskyy said: "You will reimburse us for everything you did against our state, against every Ukrainian, in full.
Thirty-three people died Thursday when Russian forces hit residential areas, including schools and a high-rise apartment block, in the northern Ukrainian city of Chernihiv, authorities said.
Mr Zelenskyy claims thousands of Russian soldiers have been killed since Mr Putin shocked the world by moving in to Ukraine, purportedly to demilitarise a western-leaning threat on his borders.
Moscow on Wednesday said that it has lost 498 troops, and Kremlin spokesman Dmitry Peskov said Mr Putin praised their sacrifice.
The Kremlin has been condemned for likening the government of Mr Zelenskyy, who is Jewish, to that of Germany in the Second World War.
While a long military column appears stalled north of Ukraine's capital Kyiv, Russian troops seized Kherson, a Black Sea city of 290,000 people, after a three-day siege that left it short of food and medicine.
Russian armoured columns from Crimea, which was annexed by Moscow in 2014, pushed deep into the region around Kherson in fighting that killed at least 13 civilians.
Nine Ukrainian soldiers were also killed, the Kherson regional administration said.
Russian troops are also besieging the port city of Mariupol, east of Kherson, which is without water or electricity in the depths of winter.
"They are trying to create a blockade here, just like in Leningrad," Mariupol mayor Vadym Boichenko said, referring to the brutal Nazi siege of Russia's second city, now called St Petersburg.
Ukrainian authorities said residential and other areas in the eastern city of Kharkiv had been "pounded all night" by indiscriminate shelling, which UN prosecutors are investigating as a possible war crime.
Oleg Rubak's wife Katia, 29, was crushed in the rubble of their family home in Zhytomyr, west of Kyiv, by a Russian missile strike.
"One minute I saw her going into the bedroom. A minute later there was nothing," Mr Rubak, 32, said in tears, amid the ruins in the bitter winter chill.
"I hope she's in heaven and all is perfect for her. I want the whole world to hear my story."
UN emergency relief co-ordinator Martin Griffiths urged Russia to allow relief workers to help Ukraine's people.
"Protect civilians, for God's sake, in Ukraine. Let us do our job", Mr Griffiths said.
Mr Putin now finds himself an international outcast, and his country the subject of sanctions that sent the rouble into further free-fall Thursday.
Russia's central bank, whose foreign reserves have been frozen in the West, imposed a 30 per cent tax on all sales of hard currency, after a run on lenders by ordinary Russians.
The unfolding financial costs were underlined as ratings agencies Fitch and Moody's slashed Russia's sovereign debt to "junk" status.
Turmoil deepened on markets more broadly. European stocks slid and oil prices approached $120 a barrel.
Russia's sporting isolation worsened as it lost the right to host Formula One races.
The International Paralympic Committee, in a decision reversal, banned Russians and Belarusians from the Beijing Winter Games.
Many Ukrainians have now fled into nearby countries, the UN refugee agency's rapidly rising tally shows.
"We left everything there as they came and ruined our lives," migrant Svitlana Mostepanenko said in Prague.
Nathalia Lypka, a professor of German from the eastern Ukrainian city of Zaporizhzhia, arrived in Berlin with her daughter, 21, and was to board a train to Stuttgart where friends were waiting.
"My husband and son stayed," Ms Lypka said. "My husband already served in the army and he had to return to duty."
Russian authorities have imposed a media blackout on what the Kremlin calls a "special military operation" that western analysts say has become bogged down.
Two liberal media groups, Ekho Moskvy radio and TV network Dozhd, said they were halting operations in another blow to independent reporting in Russia.
But Russians have still turned out for large anti-war protests across the country, braving mass arrests in a direct challenge to the president's 20-year rule.
Nearly 7,000 Russian scientists, mathematicians and academics had as of Thursday signed an open letter "strongly" protesting against Mr Putin's war in Ukraine.
Russian oil giant Lukoil on Thursday called for an immediate halt to fighting in Ukraine. It was one of the first major domestic companies to speak out against the incursion.