By Dmitry Antonov

MOSCOW (Reuters) -Vladimir Putin and Donald Trump discussed what the U.S. leader called "impressive" prospects for ties between their two countries in a phone call on Monday, the Kremlin said, adding that Russia and the United States are working on a new prisoner swap.

Putin said after the call that Russia would work with Ukraine on a memorandum about a future peace accord. Trump said Russia and Ukraine would immediately start negotiations toward a ceasefire.

Kremlin foreign policy aide Yuri Ushakov told reporters that the two leaders had not discussed a timeline for a ceasefire in Ukraine, but that Trump had stressed his interest in reaching agreements quickly.

"The presidents also spoke in some detail about the future of our relations, and President Trump, I can say, spoke quite emotionally about the prospects for these relations," Ushakov said.

"He specifically emphasized that the prospects for bilateral relations after the Ukrainian conflict is resolved look impressive, and that as the president of the United States, he sees Russia as one of America's most important partners in trade and economic matters."

Ushakov said the two countries were working out details of an exchange of prisoners jailed in Russia and the United States involving nine people on each side, although he did not say when it might take place.

Trump and Putin are both in favour of meeting in person and will assign their teams to work on preparing a meeting, Ushakov said, but no venue has been agreed.

Asked if the lifting of U.S. sanctions had been discussed, Ushakov said: "You know, Trump mentioned that the Senate, in principle, has a bill ready regarding new sanctions. But he himself is not a supporter of sanctions, but rather of reaching some agreements."

Ushakov stressed the warm nature of the conversation, saying the two men addressed each other by their first names and Putin congratulated Trump on the birth of his latest grandson.

"Trump said: Vladimir, you can pick up the phone at any time, I will be happy to answer, I will be happy to talk to you," Ushakov said.

(Reporting by Dmitry Antonov; Writing by Mark Trevelyan; Editing by Cynthia Osterman)