Ukrainian President Volodymyr Zelenskiy has welcomed four-way talks with Russia, France and Germany as meaningful and a step towards peace, a statement by his office says.
"The President of Ukraine Volodymyr Zelenskiy positively assesses the fact of the meeting, its constructive nature, as well as the intention to continue meaningful talks for two weeks in Berlin," it said.
Russian officials had earlier said it was clear the United States was not willing to address its main security concerns but was keeping the door open for further dialogue in their stand-off over Ukraine.
Kremlin spokesman Dmitry Peskov said Russia, which has built up its forces near Ukraine, would not rush to draw conclusions after the US responded on Wednesday to Russian proposals for a redrawing of post-Cold War security arrangements in Europe.
Describing tensions in Europe as reminiscent of the Cold War, Peskov said Russia needed time to review the US written response but US and NATO statements that Russia's main demands were unacceptable did not leave much room for optimism.
"Based on what our colleagues said yesterday, it's absolutely clear that on the main categories outlined in those draft documents... we cannot say that our thoughts have been taken into account or that a willingness has been shown to take our concerns into account," he said.
"But we won't rush with our assessments."
The nuanced Kremlin reaction made clear that Russia was not rejecting the US and NATO responses out of hand or closing the door to diplomacy.
The Russian foreign ministry said the best way to reduce tensions was for NATO to withdraw forces from eastern Europe but also sought to quash fears of a looming invasion.
"We have already repeatedly stated that our country does not intend to attack anyone. We consider even the thought of a war between our people to be unacceptable," said Alexei Zaitsev, a ministry spokesman.
Russian and Ukrainian dollar bonds, which have been hammered by the crisis, rose after Peskov spoke.
Russia's US-dollar-denominated RTS share index rose 4 per cent and the rouble gained more than 1 per cent against the US dollar, pulling away from a nearly 15-month low.
Though it denies planning to invade Ukraine, Russia says it wants to enforce "red lines" to protect its own security.
It presented demands in December that NATO halt any further enlargement, bar Ukraine from ever joining and pull back forces and weaponry from eastern European countries that joined the military alliance after the Cold War ended.
The written US and NATO responses were not made public but both had already rejected those demands while expressing willingness to engage on other issues such as arms control, confidence-building measures and limits on the size and scope of military exercises.
US Secretary of State Antony Blinken said his country remained committed to upholding NATO's "open-door" policy and NATO said it would not compromise its core principles.
Ukrainian, Russian, German and French diplomats discussed the conflict in eastern Ukraine in Paris on Wednesday and agreed more talks should be held in Berlin in two weeks.
Zelenskiy welcomed the meeting and "its constructive nature" and Foreign Minister Dmytro Kuleba said the agreement on more talks meant Russia was likely to remain on a diplomatic track for at least two weeks.
He said Russia's main strategy now was to destabilise Ukraine, including by using cyber attacks, and that "a military operation is something they keep in the pocket, it's not something they put ahead of other options".
Russian Foreign Minister Sergei Lavrov said there was hope of starting serious dialogue with the US but only on secondary questions and not on fundamental ones.
"The most important question is our clear position on the unacceptability of NATO's further eastward expansion and the deployment of strike weapons that could threaten Russian territory," Lavrov said in comments published on his ministry's website.
He said Putin would decide Russia's next move.
Putin, who has not spoken publicly on the crisis for weeks, has warned of an unspecified "military-technical response" - something defence analysts say could relate to missile deployments - if Russia's demands are ignored.