The US has ordered Russia to close diplomatic offices in San Francisco, New York and Washington within the next two days, in the latest round of punitive measures between the two countries that began at the end of last year.

The US secretary of state, Rex Tillerson, spoke to his Russian counterpart, Sergei Lavrov, in a phone call on Thursday. Lavrov said Moscow “regrets an escalation of tension not initiated by Russia”, according to the state-run RT news channel. A senior US administration official said the call was “professional” and that Lavrov “agreed to the sentiment that it was important to find a way to improve our relations”.

No Russians will be expelled in this latest move, and US officials said staff at the offices affected could be reassigned to other Russian diplomatic missions around the country. But they made it clear that the buildings had to be vacated and would have to be sold or have their leases ended.

In this latest retaliatory move, the state department appeared to call Moscow’s bluff, after the Kremlin claimed it wanted parity between the US and Russian missions in each other’s countries.

The closures were announced on the day the new Russian ambassador, the former deputy foreign minister Anatoly Antonov, arrived in the US. His predecessor, Sergey Kislyak, was at the centre of the scandal surrounding contacts between aides to Donald Trump and the Putin regime.

Heather Nauert, a state department spokeswoman, said the US had fully carried out Moscow’s demands to cut its staff in Russia from 1,200 to 455, to make it the same size as the Russian mission in the US. The deadline for the staff reduction was 1 September. But Nauert also announced that the US was striking back for what she said was an “unwarranted and detrimental” move by the Kremlin.

“In the spirit of parity invoked by the Russians,” Nauert said in a statement, “we are requiring the Russian government to close its consulate general in San Francisco, a chancery annexe in Washington DC, and a consular annexe in New York City. These closures will need to be accomplished by 2 September.

“With this action both countries will remain with three consulates each. While there will continue to be a disparity in the number of diplomatic and consular annexes, we have chosen to allow the Russian government to maintain some of its annexes in an effort to arrest the downward spiral in our relationship.”

Nauert said the US hoped that “having moved toward the Russian federation’s desire for parity, we can avoid further retaliatory actions by both sides and move forward to achieve the stated goal of both of our presidents”.

The buildings to be shuttered by Saturday are the consulate general and official residence in San Francisco and trade mission offices in New York and Washington.

“The buildings that are owned by the Russians will continue to be owned by the Russians,” a senior administration official said. “Then it will be up to them to determine whether they wish to sell those or dispose of them in some other way.

“We are not expelling any Russians at this time. We have informed the Russians they may reassigned to other diplomatic or consular posts in the US if they chose to.”

The official said the reduction in diplomatic ties between the two countries did not have to be irrevocable, and that Tillerson and Lavrov would meet to discuss the way forward when both are in New York in mid-September for the UN general assembly.

“I can’t really say this is permanent,” the US official said. “Certainly, if the Russians want to address some of our concerns, we would always be willing to listen and keep an open mind because our fundamental goal is to find a way to improve the relations between our countries.”

However, Dmitry Trenin, the director of the Moscow office of the Carnegie Endowment for International Peace, predicted that the cycle of retaliatory measures “won’t stop there”. On Twitter, Trenin said a “new round of US-Russian diplomatic conflict [is] in the offing”.

The new Russian ambassador, on his first day in Washington called for calm.Antonov told RIA-Novosti: “As Lenin said, hysterical impulses are of no use to us.”

The prolonged spat began last year with growing alarm in the Obama administration both about the harassment of US diplomats in Russia and concerns that Moscow interfered in the US presidential election. On 30 December, in his last few weeks in office, Obama expelled 35 Russian diplomats and locked the Russians out of diplomatic compounds in Maryland and New York.

Putin delayed a response, apparently in the expectation that the Trump administration would reverse the decision. However, Trump’s efforts to lift sanctions and explore the return of the compounds was foiled by Congress and the state department.

Putin responded at the end of last month by ordering the seizure of two US diplomatic properties and ordering the deep cuts in embassy staff. Most of those who lost their jobs were Russian nationals, and the cuts led to a suspension of non-immigrant visas to the US being issued in Russia.

A senior administration official said that visa service would be resumed shortly, “but on a much reduced scale”.

The retaliatory move by the state department comes at a time of remarkable dissonance between Trump and his secretaries of state and defence, who have taken a much tougher line on Russia. Trump has refused to be drawn into any criticism of the Kremlin, and even welcomed Putin’s announcement of cuts to the US embassy, saying it would save his administration money. The White House later said Trump was joking.