Russia said it would scale down military activity around Kyiv following "meaningful" talks in Istanbul as Ukraine's negotiators called for international guarantees for the country's security.
Ukrainian negotiator David Arakhamia also said there were now "sufficient" conditions for a direct meeting between Ukrainian President Volodymyr Zelenskyy and Russian President Vladimir Putin.
Arakhamia called for "an international mechanism of security guarantees where guarantor countries will act in a similar way to NATO's article number five -- and even more firmly".
After the face-to-face meeting in Turkey, Russian Deputy Defence Minister Alexander Fomin said talks on "the neutrality and non-nuclear status of Ukraine have moved into a practical field".
Therefore "a decision has been made to radically, by several times reduce the military activity" in the cities of Kyiv and Chernigiv, he said.
Russia's chief negotiator Vladimir Medinsky said there had been "meaningful discussion" at the talks.
It is now more than a month since Putin ordered tanks into Ukraine, hoping to cripple or oust the democratic government in Kyiv.
The fighting has already forced more than 10 million from their homes and according to Zelenskyy has killed an estimated 20,000 people.
But Tuesday's announcements offered some hope.
US President Joe Biden said he would discuss the "latest developments" with the leaders of Britain, France, Germany and Italy at 1315 GMT.
European stock markets lifted and oil prices fell by five percent as supply fears eased while the ruble surged 10 percent against the dollar.
But fighting still raged in many parts of the country.
Adding to the toll, Ukraine said seven people were killed by a Russian strike on a regional government building in the southern port city of Mykolaiv.
Ukraine says it has recaptured territory in recent days, including the suburban town of Irpin outside Kyiv -- an important gateway to the capital.
It has also resumed evacuations from areas in the south of the country occupied by Russian forces.
Turkish President Recep Tayyip Erdogan had opened the talks at the sprawling Dolmabahce palace, recognising "legitimate concerns" on both sides but urging them to "put an end to this tragedy".
Russian oligarch and Chelsea Football Club owner Roman Abramovich, who has been hit by Western sanctions, was also in attendance.
The Kremlin said he was acting as an intermediary and denied reports that he had been poisoned during a previous round of negotiations in Ukraine.
"This is part of information sabotage, part of an information war," Kremlin spokesman Dmitry Peskov told journalists.
Putin has demanded the "demilitarisation and denazification of Ukraine", as well as the imposition of neutral status and recognition of the Donbas and Crimea as no longer part of Ukraine.
The West has imposed crushing economic sanctions in response to the invasion and several Western companies have pulled out of Russia.
Russia hit back on Tuesday, insisting that it would only be accepting payment for gas deliveries to the EU in rubles even though G7 ministers called this arrangement "unacceptable".
"Nobody will supply gas for free. This is just impossible. And it can only be paid in rubles," Peskov told reporters.
Russia also said it was expelling 10 diplomats from Estonia, Latvia and Lithuania in a tit-for-tat move after the Baltic countries expelled Russian diplomats over the conflict.
While Ukraine's forces are counterattacking in the north, they are struggling to retain control of the southern port city of Mariupol.
Russian forces have encircled the city and have embarked on a steady and indiscriminate bombardment, trapping an estimated 160,000 people with little food, water or medicine.
At least 5,000 people have already died, according to one senior Ukrainian official who estimated the real toll may be closer to 10,000 when all the bodies are collected.
Zelenskyy said the Russian siege constituted a "crime against humanity, which is happening in front of the eyes of the whole planet in real time".
Ukraine's foreign ministry called the situation "catastrophic," saying Russia's assault from land, sea and air had turned a city once home to 450,000 people "into dust".
France, Greece and Turkey are hoping to launch a mass evacuation of civilians from Mariupol within days, according to French President Emmanuel Macron, who is seeking agreement from Putin.
Western powers say they have seen evidence of war crimes, which are already being investigated by the International Criminal Court.
On Monday, Ukraine's prosecutor general, Iryna Venediktova, said there was proof that Russian forces have used banned cluster bombs in the southern Odessa and Kherson areas.
Biden has expressed his "moral outrage" at the conduct of the war, and ruffled feathers over the weekend by suggesting Putin "cannot remain in power".
He has since denied seeking regime change and swatted away concern that his remarks would ratchet up tensions with Putin.
"I don't care what he thinks," Biden said on Monday.
The conflict has also raised fears over nuclear safety after Russia seized several facilities, including Chernobyl, the site of the world's worst nuclear disaster.
The chief of the UN atomic watchdog, Rafael Grossi, was visiting Ukraine on Tuesday to discuss the "safety and security" of nuclear sites there.
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