The United States has told Russia to close its consulate in San Francisco, in retaliation for Moscow's demands that the size of the US mission in Russia be cut, according to the State Department.

The announcement on Thursday also included a demand for a reduction in Russian diplomatic presence in Washington, DC, and New York by Saturday with the closure of a chancery annex in Washington, DC, and consular annex in New York.

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.

In spirit of parity, we require #Russia to close its consulate in SF, chancery annex in DC, and consular annex in NYC by Sep. 2. pic.twitter.com/8YeFncDO4l — Department of State (@StateDept) August 31, 2017

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

"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," Nauert said.

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

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In response, Russia's foreign ministry said in a statement that Moscow "will closely study the new measures announced by the Americans, after which our reaction will be conveyed".

Russian Foreign Minister Sergey Lavrov also held a phone conversation with his US counterpart, Rex Tillerson, and expressed his regret about "the escalation of tensions" between the two countries.

The dispute began when former US President Barack Obama expelled 35 Russian diplomats in December over allegations of Russian interference in last year's presidential election.

"This is a back-and-a-forth that has been going on," Al Jazeera's Kimberly Halkett, reporting from Washington, DC, said.

"Certainly this is a stepping-up by the US in terms of the tit-for-tat relationship that has been going on, and many would see deteriorating, in recent months," she added.

In order to deal with the reduction of staff in Russia, Washington said last week it would have to sharply scale back visa services, a move that will hit Russian business travellers, tourists and students.

The Russian consulate in San Francisco handles work from seven states in the western US.

There are three other Russian consulates separate from the embassy in Washington, DC. They are in New York, Seattle and Houston.