The U.S. said it is hoping for improved relations between the two countries and increased cooperation "on areas of mutual concern".
The State Department announced on Thursday that it would close the USA consulate in San Francisco, along with its annexes in Washington and NY, in retaliation for Moscow expelling us diplomats.
The US sanctions were imposed in response to alleged Russian meddling in the 2016 US presidential election and to punish Russia further for its 2014 annexation of Crimea from Ukraine.
"The United States has fully implemented the decision by the Government of the Russian Federation to reduce the size of our mission in Russia".
The White House did not immediately respond to a request for comment on the decision.
"As you know, it takes two to tango", Lavrov said.
The Russian offices must close by Saturday.
The move signals worsening of ties between the two countries which have reached a new low in the post-Cold War era. "I would like to point out it was not us who initiated this exchange of sanctions, but the (Barack) Obama administration".More news: Powerful Explosion Detected In North Korea In Possible Nuclear Weapons Test
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"We're responding in this instance to the Russian desire for parity in the diplomatic relationship", the official told reporters on background. The Kremlin has denied the allegations.
In addition, John Heffern - acting Assistant for European affairs at the State Department - met with Russia's Deputy Chief of Mission Dmitry Zhirnov and relayed the decision.
The official says the closures affect Russia's consulate general in San Francisco and an official residence there.
That move was in turn a response to US sanctions imposed on Russia, which were enacted by Congress in response to Russian election interference.
The first punishment, handed down by President Obama, forced Russia to move out of two diplomatic compounds in the US and send home 35 Russian diplomats.
Tillerson and Lavrov also agreed to a meeting in September, according to the official.
It urged the United States to stop the "gross violations" of global law and the encroachment on the immunity of Russia's diplomatic institutions. Those activities may continue in other US cities.
A spokeswoman for the ministry, Maria Zakharova, said the search, which the United States has not confirmed, would "create a direct threat to the security of Russian citizens".