Kremlin spokesman Dmitry Peskov told reporters on Wednesday that "of course" Russia floated proposals such as this one to the US.
"Moscow systematically advocated for a resumption of the dialogue, for an exchange of opinion and for attempts at finding joint solutions," Peskov said. "But, unfortunately, it saw no reciprocity."
Peskov said Russia's proposals had come through in parts and a summary of the offer went through diplomatic channels.
News of the plan first came to light in a BuzzFeed News report
after the outlet obtained a document which outlined the proposal a top Russian diplomat made directly to the US State Department.
Asked about the report, State Department spokeswoman Heather Nauert would neither confirm nor deny its accuracy. Nauert said in general terms that the US and Russia share the goal of improving diplomatic relations between the countries.
A Russian official confirmed to CNN that the document was authentic.
"We are sorry to hear that documents keep leaking from the (Trump) administration, though it shows that Russia keeps doing its best to normalize relations," the official said.
Earlier Tuesday, Under Secretary of State Tom Shannon met with his Russian counterpart in Finland. The meeting was their third of the year to discuss so-called "irritants" in the relationship. Nauert said the meeting provided an opportunity to "raise questions or concerns," but did not say if the two had resolved anything.
The proposal, BuzzFeed wrote, called for the US to restore all channels -- diplomatic, military and intelligence -- that had been cut following Russia's invasion of Ukraine
and intervention in Syria.
In the coming months, the proposal called for Russia and the US to collaborate on information security, Afghanistan, Iran, Ukraine, North Korea and eventually a full face-to-face meeting between the top national security officials of the two nations.
Relations between the United States and Russia have soured considerably since the opening of the Trump administration, when many expected Trump might bring the nations closer together as he said repeatedly was his goal during the campaign.
Russian military involvement in Ukraine and Syria, as well as the US intelligence community's conclusion
that Russian President Vladimir Putin personally ordered an attempt to meddle in the 2016 US presidential election, has cast a shadow on the US side over the potential rapprochement.
The US under then-President Barack Obama increased sanctions
on Russia following the country's alleged election interference, and moved to shutter some of the Kremlin's facilities in the US.
Trump met with Putin face-to-face in a scheduled meeting
at the G20 summit in July then spoke again during an unannounced conversation
at a dinner for world leaders during the summit. Trump went on to propose
a joint US-Russia cyber effort, then after sustained criticism of the proposal, Trump said he knew "it can't" happen.
Russia responded in kind to the US' sanctions after several months delay and ordered large cuts
in the US diplomatic staff in Russia. Around the same time, Trump signed a bill
putting more sanctions on Russia and restricting his ability to lift them.
He also thanked Putin for forcing the US to reduce its diplomatic staff in a comment
the White House later described as sarcastic. Before Moscow's deadline for the US to reduce its diplomatic staff in Russia, the US ordered
the closure of three Russian facilities in the US.