The US President had said that he intends to invite Russia, Australia, South Korea and India to a meeting of the G7 nations.
Russia had been included in the gathering of the world’s most advanced economies since 1997, but was suspended in 2014 following its invasion of Ukraine and annexation of Crimea.
The Kremlin said on Monday that Mr Trump told Mr Putin about his idea, but it did not offer any details of the discussion or say whether the Russian leader accepted the invitation.
The White House confirmed the call, saying the two men “discussed the latest efforts to defeat the coronavirus pandemic and reopen global economies”.
“President Trump also reiterated the need for effective arms control,” the White House said, and added: “Additionally, the two leaders discussed progress toward convening the G7.”
The meeting was due to go ahead next month, but Mr Trump said it will now be postponed until the autumn.
He told reporters the current make-up of the group is “very outdated” and does not properly represent “what’s going on in the world”.
The current G7 members are Canada, France, Germany, Italy, Japan, the UK and the US.
Canadian prime minister Justin Trudeau said on Monday that Russia will not be included in the G7, disagreeing with Mr Trump.
Mr Trudeau noted Moscow’s “continued disrespect and flaunting of international rules and norms”.
The Kremlin also said that Mr Putin thanked Mr Trump for a batch of US ventilators sent to Russia and the two leaders talked about steps their countries have taken to combat the coronavirus outbreak.
The Russian president also congratulated Mr Trump on Saturday’s launch of two US astronauts aboard the Dragon spacecraft built by Elon Musk’s SpaceX company, the Kremlin said.
The launch put the US back in the business of sending astronauts into orbit from home soil for the first time in nearly a decade — during which time it relied on Russian spacecraft to deliver its astronauts to the International Space Station.
The Kremlin said the two leaders spoke of the development of mutually beneficial co-operation in space and also talked about the need to intensify a US-Russian dialogue on strategic stability and steps to enhance mutual trust in the military sphere.