Moscow said a date for talks was being worked on, after Ukrainian President Volodymyr Zelensky proposed holding fresh negotiations over the weekend.
Efforts to reach a diplomatic solution to the three-year-long war have stalled after US President Donald Trump forced the two sides to open direct talks after he returned to the White House in January.
The two sides last met more than a month ago in Istanbul, exchanging draft ideas of what a peace deal could look like.
"We now need to exchange views and hold negotiations on these two drafts, which are currently diametrically opposed. A lot of diplomatic work lies ahead," Kremlin spokesman Dmitry Peskov told reporters, including AFP, in a briefing call.
The talks have so far resulted only in prisoner exchanges, with momentum for a ceasefire having sapped.
Trump, who has expressed mounting frustration with Putin, last week gave the Russian leader a 50-day ultimatum to make a deal or face massive economic sanctions.
Zelensky on Saturday called for talks to take place this week. A senior Ukrainian official told AFP they might take place "from Tuesday to Thursday" and "most likely in Istanbul."
Moscow said it was ready, but that there was no agreement for when the next round would take place yet.
"As soon as there is final agreement on the dates, we will inform you immediately," Peskov said.
Russia last month demanded Kyiv's army retreat from four Ukrainian regions Moscow claimed to annex in September 2022, but does not have full control over, as well as reject all forms of Western military support.
Kyiv dismissed it as an unacceptable ultimatum, and has at times questioned the point of further negotiations if Moscow was not willing to make concessions.
Ukraine called for an immediate ceasefire and for Moscow to respect its NATO and EU ambitions.
- French foreign minister in Kyiv -
Russia has fired a record number of drones and missiles at Ukrainian cities in recent weeks, deadly attacks that Kyiv says show Moscow is not serious about halting its invasion.
Two people were killed across the country in the latest wave, Zelensky said on Monday, calling it an "assault on humanity."
French Foreign Minister Jean-Noel Barrot arrived in the capital for a surprise visit while rescuers were still sifting through the rubble.
He later held talks with Zelensky, discussing air defence, sanctions and weapons production, the Ukrainian president said in a social media post.
Six districts of Kyiv came under attack on Monday, sparking fires at a supermarket, multiple residential buildings and a nursery, authorities said.
An AFP reporter saw damage to multiple buildings, as well as debris and shattered glass on streets.
The entrance to a metro station where civilians were sheltering from the barrage was also damaged.
"The shelters themselves are no longer entirely safe, as the metro station behind me, which is being used as a shelter for the people of Kyiv, has been targeted," Barrot said while visiting the damaged station.
Russia's invasion has killed tens of thousands, forced millions to flee their homes and devastated much of eastern Ukraine.
Russia launched 450 drones and missiles in the overnight attack, according to Ukraine's air force.
The strikes, also using hypersonic missiles, targeted Ukraine's military facilities, the Russian army said, claiming it had destroyed three US-made Patriot air defence launchers.
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