Russia is angry that Washington is still barring its diplomats from using two compounds in the states of New York and Maryland after then president Barack Obama in December ordered the ban on access in response to suspected Russian meddling in the US election.
"We consider it absolutely unacceptable to place conditions on the return of diplomatic property, we consider that it must be returned without any conditions and talking," Kremlin spokesman Dmitry Peskov told journalists.
Diplomats quoted by Russian news agencies said the issue of the residential complexes would be on their agenda.
The talks between Shannon and Ryabkov were earlier scheduled for June but Russia cancelled them, citing new US sanctions linked to the conflict in Ukraine.
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When President Vladimir Putin and US counterpart Donald Trump met for the first time at the G20 summit in Hamburg this month, the Kremlin strongman raised the question "quite unambiguously," Peskov said.
He added that "we still hope our American colleagues will show political wisdom and political will."
He said the measures were in response to US intelligence reports of Russian hacking and an alleged influence campaign to sway the US presidential election in Trump's favour, describing the compounds as used by Moscow for "intelligence- related purposes."
At the time Putin held off from retaliating, saying he would wait to see how Trump reacted after he came into the White House.
But hope that Trump will soon follow up on campaign pledges to boost relations have fizzled as any ties to Moscow have become toxic for the White House amid a maelstrom of US investigations into possible collusion between Russia and the Trump campaign.
Foreign Minister Sergei Lavrov said last week: "If Washington decides not to solve this issue, we will have to take counter actions."
Foreign Ministry spokeswoman Maria Zakharova complained last week that the US was also refusing to issue visas for Russian diplomats to replace those expelled.