The decision to scale back operations around the capital, Kyiv, and the northern city of Chernihiv is the first sign of tangible progress.
But it is unclear how extensive any reduction in military activity might be, and Ukraine remains sceptical.
Russia had already refocused its campaign on Ukraine's eastern regions.
It has suffered a series of setbacks to the north-west of the capital, Kyiv, and is also seeking to capture a land corridor which stretches along the south coast to the Russian border.
President Volodymyr Zelensky. however, said he saw no reason to believe the words of some Russian representatives.
"We can say that the signals... are positive, but those signals do not drown out the explosions or Russian shells," he said in a video address late Tuesday.
Officials in Washington said they had already seen the Russians draw away from Kyiv, but they were still pounding the capital with air strikes. The US said it had little confidence that the announcement marked any significant shift or meaningful retreat.
The US had not seen "signs of real seriousness" from Russia in pursuing peace talks, said Secretary of State Antony Blinken, who pointed to the continued "brutalisation" of Ukraine's people.
During the talks in the Turkish city of Istanbul, Ukraine proposed to become a neutral state in exchange for security guarantees. A key aim of Russia's invasion was to stop Ukraine joining the Nato alliance and Russian officials said the talks had moved to a practical stage.
Deputy Defence Minister Alexander Fomin, who was in Istanbul, told Russian TV that as "Ukraine's neutrality and non-nuclear status and security guarantees" had progressed, the defence ministry had taken the decision to cut its operations dramatically in the two areas to "create the necessary conditions for further negotiations and for the signing of the aforementioned agreement".
Ukrainian negotiator Oleksandr Chaly told reporters that its offer of neutrality was a chance to "restore the territorial integrity and security of Ukraine through diplomatic and political means". Ukraine's aim was to "fix its status as a de facto non-bloc and non-nuclear state in the form of permanent neutrality".
Russian forces have encircled Chernihiv, where officials say up to 400 people have been killed and some 130,000 residents are without heating, electricity or water supplies.
UK Prime Minister Boris Johnson's spokesman said that Russia had twisted the knife in Ukraine and that "we must judge Putin's regime by their actions not their words".
Russia's chief negotiator, Vladimir Medinsky, said talks had been "meaningful" and Ukraine's proposals on neutrality would be put to President Vladimir Putin, holding out the possibility of a summit involving President Zelensky. However, he made clear that before that could happen a treaty would have to be drafted and approved by negotiators, and then signed by foreign ministers.
"This is not a ceasefire but this is our aspiration, gradually to reach a de-escalation of the conflict at least on these fronts," Mr Medinsky told Russian state news agency Tass.