Vladimir Putin says that thanks to Donald Trump, the US and Russia are starting to align.
Putin says he had "great respect" for Trump and was willing to meet him and it would be "quite possible".
"In general, thanks to President Trump, relations between Russia and the United States are beginning to level out in some ways."
Speaking to reporters in Minsk, he also says Russia plans to cut military spending in the long term, according to state media.
Russia is facing budgetary pressures due to increased defence spending, which has fuelled inflation, he says.
Moscow is also ready to hold a new round of peace negotiations with Ukraine, he says.
They could potentially take place in Istanbul, Turkey, although the time and venue had yet to be agreed.
Putin adds Russia is ready to return the bodies of 3,000 more Ukrainian soldiers.
At negotiations in Istanbul on 2 June, Ukraine and Russia agreed to exchange a total of 12,000 bodies of fallen soldiers.