"When our presidents spoke on the phone, Mr Trump proposed having the first meeting in Washington, in the White House", Mr Ushakov told reporters at a briefing.
The two sides have had no preparatory conversations since the March 20 call in which the leaders discussed the idea due to their tit-for-tat expulsions of diplomats over the poisoning of a former spy in the U.K., Ushakov said.
US President Donald Trump will celebrate on April 17 and 18 a summit in Florida with Japanese Prime Minister Shinzo Abe, which is marked by negotiations with North Korea, as announced on Monday White House.
Ushakov expressed confidence that Washington would not withdraw the invitation, which was extended before the mutual expulsion of U.S. and Russian diplomats over a spy attack case case.
Why does Trump never criticize Putin?
In his remarks from the White House portico, President Trump attributed the day to his wife's hard work.
She added that the administration had no further comment on the matter. "I hope the Americans won't abandon their proposal to discuss the possibility of holding the summit", he said.
Some politicians from Mr Trump's Republican party had criticised him for making the congratulatory call to Mr Putin.
Kremlin spokesman Dmitry Peskov, however, told CNN that reports that Trump had invited Putin to the White House were not correct.
Then U.S. President congratulated Putin on his victory in the presidential election.
Last week, Russia announced it would expel 60 American diplomats and close the USA consulate in St. Petersburg - a tit-for-tat reaction to the US decision to order Russian diplomats out over the poisoning of an ex-Russian spy in Britain.
Other experts stress the aggressive moves that the Trump administration has taken against Russian Federation, from expelling diplomats and closing consulates to a new round of sanctions. The talks were a prelude to Trump's first meeting with Putin at the Group of 20 summit last July.