The United States is requiring Russia to close its consulate in San Francisco and two annex buildings in Washington, DC and New York City, the State Department has announced.

The move is in response to the Kremlin's decision to shrink the US diplomatic mission in Russia.

Last month Russia ordered the US to cut its diplomatic and technical staff in Russia by more than half, to 455 people, after Congress overwhelmingly approved new sanctions against Russia.

"We believe this action was unwarranted and detrimental to the overall relationship between our countries," State Department spokeswoman Heather Nauert said in a statement.

"In the spirit of parity invoked by the Russians, we are requiring the Russian Government to close its Consulate General in San Francisco, a chancery annex in Washington, DC, and a consular annex in New York City," Ms Nauert said.

"These closures will need to be accomplished by 2 September."

Russian Foreign Minister Sergei Lavrov expressed regret about the move during a phone call with his US counterpart Rex Tillerson, his ministry said.

"Moscow will closely study the new measures announced by the Americans, after which our reaction will be conveyed," the Russian foreign ministry said in a statement.