(ABC News) -- A Russian official said after a high-level meeting with Trump administration officials that the two countries have "almost" reached a deal for the U.S. to return two diplomatic compounds to Russian control.

Russian Deputy Foreign Minister Sergei Ryabkov had just left the meeting at the U.S. State Department early Monday evening when he responded to a shouted question about whether the two countries are close to a deal on the Russian compounds.

"Almost, almost," he said.

Ryabkov met with U.S. Under Secretary of State Tom Shannon in Washington –- the highest level meeting since the two countries' presidents, Donald Trump and Vladimir Putin, met at the G-20 summit in Hamburg, Germany, on July 7.

Monday's meeting comes as the Trump administration faces intense pressure from Russia on one side and the U.S. Congress on the other over the fate of the two compounds, or dachas, in New York and Maryland.

The State Department has not commented on the meeting.

The Obama administration in December 2016 cut off Russia’s access to the dachas and expelled 35 Russian diplomats in response to Russia's cyberattacks on the 2016 U.S. election.

Russia has been losing patience with the Trump administration over the issue, threatening to retaliate if the compounds are not returned soon.

"It appears that the Russian side has no choice, it is time to retaliate," the chairman of Russia's Federation Council's foreign affairs committee told Sputnik, a Russian state-owned news agency.

Kremlin spokesman Dmitry Peskov took a slightly softer tone, telling reporters that Russia hopes the White House can still find the "political wisdom and political will" to return the dachas.

But the ranking Democrat on the Senate Foreign Relations Committee said any action toward returning the dachas would be "a major affront to Congress." Sen. Ben Cardin, D-Maryland, is just the latest to express his opposition; two bipartisan groups of Senators have previously written letters to the Trump administration, urging them not to return the compounds, including Republicans Marco Rubio, Lindsey Graham, and Johnny Isakson.

Security members stand guard, Dec. 31, 2016, at a Russian compound in Upper Brookville, N.Y., one day after the compound was closed. (Eduardo Munoz/AFP/Getty Images)

The Senate passed new sanctions legislation in June that would codify existing sanctions, implement new ones and force the Trump administration to seek Congressional approval before it can change any sanctions -- including returning the compounds. The legislation is currently awaiting a vote in the House, where it is being held up.

Despite the threats from Russia and strong Congressional opposition, the Trump administration does appear to be considering returning the dachas. As deputy assistant to the President, Sebastian Gorka said on CNN last Thursday, "We want to give collaboration, cooperation a chance."

The White House may ask for something in return. Sputnik reported that a senior White House official told the Russian state-owned agency that the properties would be given back only if it receives something back from Moscow, which Russian Foreign Minister Sergei Lavrov blasted as "daytime robbery."

For the U.S., the set of grievances includes an end to Russian harassment of U.S. diplomats and a lift on the ban of Americans adopting Russian children.

Ryabkov canceled his last scheduled meeting with Shannon in June –- while Shannon was traveling in Europe on his way to St. Petersburg –- because the U.S. announced updated sanctions over Russian aggression in Ukraine a couple days prior. The two men met once before in New York in May as the Trump administration has sought better relations with Moscow.