US President Donald Trump has invited his Russian counterpart to visit Washington "in the fall" and the trip is already being discussed, the White House said.

Trump "asked Ambassador John Bolton to invite President Putin to Washington in the fall," White House press secretary Sarah Huckabee Sanders said on Thursday. "Those discussions are already underway."

Trump and Putin met on Monday in Helsinki, Finland, their first summit since Trump took office in January 2017. The US president has faced a withering wall of opposition at home, however, both from Democrats who have accused him of "collusion" with Russia during the 2016 election and some in his own party who consider Russia an enemy not to be talked with.

Hours before Sanders made the announcement, the Senate voted unanimously to "refuse to make available any current or former diplomat, civil servant, political appointee, law enforcement official or member of the Armed Forces of the United States for questioning by the government or Vladimir Putin."

The non-binding resolution was in response to an offer made by Putin in Helsinki, for US and Russian officials to interrogate suspects under a 1999 treaty on law enforcement cooperation.

Putin has visited the US seven times previously, beginning with the UN Millennium Summit in September 20000. His most recent visit was in September 2015, according to the State Department, where he met then-President Barack Obama on the sidelines of the UN General Assembly meeting in New York.