The US has order Russia to close its consulate in San Francisco and scale back its diplomatic presence in Washington and New York, a move set to further sour relations between the two countries.

The US administration of President Donald Trump said the move was in response to the Kremlin forcing a cut in US diplomatic staff in Moscow.

The Trump administration said the move - which includes the closure of Russia's "chancery annex" in Washington and a "consular annex" in New York - constituted its response to the Kremlin's "unwarranted and detrimental" decision to force the US to cut its diplomatic staff in Russia.

"The United States is prepared to take further action as necessary and as warranted," State Department spokeswoman Heather Nauert said.

In July, Russia ordered Washington reduce its diplomatic staff by 755 people. Moscow forced the cut in retaliation over US sanctions.

Rex Tillerson, the US secretary of state, said at the time that Washington would respond by September.

The Russian offices must close by Saturday.

There was no immediate reaction from the Russian government.

But given the back-and-forth nature of the escalating tensions over the past year, it was likely the Kremlin will feel compelled to respond by taking further action against the US.