White House press secretary Sarah Huckabee Sanders says the White House was among "a number of potential venues" discussed in the phone call.
Since the March 20 phone call, Washington expelled 60 Russian diplomats and closed a Russian consulate over allegations that Russia was behind the poisoning of former Russian spy and his daughter in Britain.
President Trump on Tuesday told the leaders of the Baltic States - Latvia, Lithuania, and Estonia - that he has been tough on threats from Russian Federation, but said a better relationship with President Vladimir Putin would be "a good thing".
He told reporters in Moscow that Trump had suggested a meeting at the White House, saying, "This is a rather positive idea".
"Trump called Putin last month to congratulate him on his election victory and told reporters he believed he and Putin would meet "in the not too distant future".
'It was Trump himself who proposed holding the meeting, ' Ushakov said. The U.S. intelligence community has assessed Putin directed an influence campaign aimed at the 2016 election that brought Trump to office.
"After the conversation, which was constructive and business-like and touched upon many issues, there was another breakdown in our bilateral relations, 60 diplomats were expelled, our consulate was closed and Russian Federation had to furnish a tit-for-tat response to that", Ushakov told TASS.
Just as Trump has shown a curious reluctance to criticize Putin, even when the two countries are ejecting each other's diplomats, the Kremlin and the Russian news outlets it controls have often avoided criticizing Trump directly.
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The space station has been slowing down and when it can't go fast enough to stay in orbit, it will reenter the earth's atmosphere. The Aerospace Corp. says it could land along a strip of the US that includes the southern Lower Peninsula of MI .
"Nobody has been tougher on Russia", Trump said during a luncheon meeting with Baltic leaders who have said they are anxious about the threat of Russian expansionism.
In calling Mr Putin, Mr Trump ignored the explicit advice of his national security advisers. She said the administration had no further comment. That should never be the objective.
Russia's disclosure of the invitation came the day before the leaders of three Baltic countries - Latvia, Lithuania and Estonia - were to visit the White House.
As president, Trump met Putin in July at the Group of 20 summit in Germany and then briefly at the Asia-Pacific Economic Cooperation summit in Vietnam in November.
Putin has been to other parts of the US frequently in recent years, including a visit to the Bush family compound in Maine.
Baltic leaders have increased their criticism of Russian Federation since it annexed part of Ukraine in 2014, but their White House visit comes at an unusual time for U.S. Putin's meetings with Obama occurred at worldwide summits and along the sidelines of the United Nations gathering in NY.
Mr Obama met former Russian president Dmitry Medvedev at the White House in 2010, when the pair also chowed down on burgers at a popular hamburger joint outside the capital.