Lavrov, in a telephone conversation with Tillerson, also said it was unacceptable that US authorities had removed Russian flags from its seized diplomatic buildings in the United States, the ministry said.
Also on Thursday, the Russian parliament's lower house, the Duma, cancelled a visit to the USA by a group of lawmakers planned for this month, a Duma spokeswoman told AFP.
The Foreign Ministry added that the actions of United States officials contradicted the statements of Washington about an intention to normalize bilateral relations.
Washington ordered the shutdown of the Russian diplomatic missions after the Kremlin demanded that the USA slash staff numbers at its missions in Russia.
In early August this year, US President Donald Trump signed a bill imposing new sanctions on Russian Federation - and also on Iran and North Korea - simultaneously stating that the motion was "seriously flawed" and blasting the US Congress for applying pressure to see the bill signed into law.More news: Kobe Steel chief admits scandal has hit trust as vehicle checks spread
"The flags at the former Russian consular properties in San Francisco were respectfully lowered and are safely stored within each of the buildings", a State Department official said in e-mails to reporters.
The development came two days after Foreign Minister Sergei Lavrov told his American counterpart, Rex Tillerson, that the Russian diplomatic properties had been "illegally seized" by the USA government, demanding their return to Moscow's embassy in Washington.
"Such steps only complicate US-Russian dialogue", Antonov said in televised remarks.
A third Russian government property in NY was a suite in commercial building and did not have a flag, the State Department official added.
A spokeswoman for the U.S. Embassy in Moscow said Washington hoped that complying with the Russian requirements would mean both countries could stop trading retaliatory measures, RIA later reported.