MOSCOW (AFP) - Russia said the FBI planned to carry out a search of its San Francisco consulate, which Washington ordered closed along with two other facilities as part of a diplomatic slugging match between the two powers.

Russian foreign ministry spokesman Maria Zakharova said on Friday (Sept 1) that the search was set for Saturday and accused the US authorities of threatening the "security" of Russian citizens and violating diplomats' immunity.

Mysterious black smoke was seen rising from a chimney at the consulate, as firefighters confirmed its occupants were burning unidentified objects on the eve of the mission's closure.

Washington on Thursday ordered the Russian consulate in San Francisco, and two buildings in Washington and New York that house trade missions to be shut down by Saturday, in a retaliatory move after the Kremlin demanded the US slash staff numbers at its Russian diplomatic missions.

The spat between the two nuclear-armed powers is another blow to US President Donald Trump's pledge to try to improve relations with Russia's Vladimir Putin.

Zakharova said in a statement that the FBI intended to carry out a search of the San Francisco consulate "including of the apartments of employees who live in the building and have immunity," forcing them and their families to leave for up to 12 hours.

"We are talking about invasion into a consulate and the accommodations of diplomatic staff," Zakharova said. "The demands of the US authorities create a direct threat to the security of Russian citizens."

"We express a resolute protest over Washington's actions that ignore international law," she said, adding that "we reserve the right to take retaliatory measures."

The US ordered the closures in a retaliatory move after the Kremlin demanded Washington slash staff numbers at its Russian diplomatic missions to 455 personnel with a deadline that ran out on Friday.

"The United States has fully implemented the decision by the government of the Russian Federation to reduce the size of our mission in Russia," State Department spokeswoman Heather Nauert confirmed in a statement.

Washington said it hoped the two sides "can avoid further retaliatory actions" and improve ties but warned it was "prepared to take further action as necessary and as warranted."

Firefighters were called to the consulate on Friday in response to alarmed - or intrigued - phone calls from citizens, but later clarified there was no cause for concern.

San Francisco fire department spokesman Mindy Talmadge told AFP that consulate employees "must be" in the middle of burning unknown items.

'TAKES TWO TO TANGO'

But top diplomat Sergei Lavrov avoided blaming the Trump administration for the latest tensions and laid the guilt squarely at the door of his predecessor Barack Obama.

"We are open even now for constructive cooperation where it corresponds to Russian interests," Lavrov said on Friday.

"But it takes two to tango and so far our partner is, again and again, doing an individual break dance."

Lavrov is to meet his US counterpart Rex Tillerson in September in New York.

The fresh diplomatic spat is the latest twist in tortured ties between the US and Russia, which have slumped to their lowest point since the Cold War following the Kremlin's seizure of Crimea from Ukraine in 2014.

The West slapped punishing sanctions on Russia over its meddling in its ex-Soviet neighbour, sparking a revenge embargo from Moscow against agricultural products.

'HYSTERICAL IMPULSES NOT USEFUL'

Last year tensions ramped up again after the US intelligence community accused Putin of masterminding a hacking and influence campaign to tip the presidential vote in favour of Trump.

In the waning days of his tenure, Obama hit out at Russia over the allegations by turfing out 35 diplomats and closing two of Moscow's diplomatic compounds.

Moscow initially held off from retaliating but when Congress passed new sanctions tying up Trump's hands, the Kremlin decided to belatedly strike back and ordered the US staff cut.

Any impression that he is cosying up to Russia has become politically toxic for Trump amid a string of probes into potential collusion between his team and the Kremlin.

Thursday's announcement by the State Department came as Russia's new ambassador to Washington, Anatoly Antonov, arrived in the US capital to take up his post, Russian news agencies reported.

"Right now we need to calmly examine (this situation). We should act calmly and professionally," Antonov told RIA-Novosti. "As Lenin said, hysterical impulses are of no use to us."

Antonov's predecessor Sergei Kislyak is one of the figures at the centre of the scandal over alleged Russian meddling in the November election in a bid to help Trump beat Democrat Hillary Clinton.