Trump, who has been accused of cozying up to Putin, and whose presidential campaign is under investigation over Russian hacking, also said it "would be a good thing, not a bad thing", if the United States got along with Russia.
White House press secretary Sarah Huckabee Sanders says the White House was among "a number of potential venues" discussed in the phone call.
However, their governments didn't have time to start arranging a meeting before the United States joined Britain and more than two dozen allies in sanctioning Russia over the nerve-agent poisoning of a Russian ex-spy in England, Ushakov said.
Trump says there was no collusion between his campaign and Russian Federation.
He told reporters in Moscow that Trump had suggested a meeting at the White House, saying, "This is a rather positive idea". He was welcomed by President George W. Bush in 2005.
During the March 20 phone call, Trump congratulated Putin on his re-election victory widely criticized as not free and fair.
Russian Federation responded by expelling 60 U.S. diplomats and publicising the content of the phone call.
Ushakov voiced hope that tensions resulting from the diplomatic expulsions wouldn't derail discussions about a summit. Those moves were in retaliation to Russian interference in the 2016 USA presidential election and the recent poison attack on an ex-Russian spy in London. "The only reason you should do it is if you're going to obtain a concrete objective that serves America's national security interest before the meeting", he said.More news: Trump administration to hold more pregnant women in ICE detention
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"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. That should never be the objective. She said the administration had no further comment.
See all of the daily White House Daily Chronicles HERE. The three North Atlantic Treaty Organisation nations are seen as a bulwark against Russia's aspirations of extended influence west of its border.
Mr Trump has met Mr Putin twice as President, at the G20 summit in Germany a year ago and briefly at the Asia-Pacific Economic Co-operation summit in Vietnam in November.
But Trump has expressed skepticism over USA defense commitments overseas, and used the same press conference on Tuesday to say he wants US involvement in Syria to end as soon as the Islamic State is defeated.
It has been awhile since Putin visited the White House.
But during Mr Obama's presidency, meetings between the USA president and Russian leader 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.