The Justice Department has acknowledged that Sessions was at the Mayflower Hotel event in Washington, but said there were no private or side conversations that day.
In addition, lawmakers expect former FBI Director James Comey to appear before them sometime in the coming weeks to give testimony in a public congressional hearing.
Delving into a political quarrel over the most recent subpoenas in the US House Intelligence Committee's Russian Federation test, US President Donald Trump on Thursday backed endeavors to examine activities by US security and different authorities under past president Barack Obama.
Epshteyn, who grew up in Moscow, worked a short time in the White House press office. No date for Comey's testimony has been set.
While media outlets have been focusing on the Russian contacts pursued by Trump's son-in-law and senior adviser, Jared Kushner, there are few people closer to the President than his personal attorney, who has advised him for years.
Another senior committee aide said any subpoenas related to the unmasking issue would have been sent by committee Chairman Rep. Devin Nunes, R-Calif., who recused himself from the Russian Federation investigation after being criticized for being too close to the White House.
Top House Democrats began calling for Nunes to recuse himself from the panel's investigation into Russian Federation in March, following the revelations that he had met on White House grounds with a source who showed him secret United States intelligence reports. He remains chairman, but Rep. Mike Conaway, R-Texas, is now leading the probe. According to committee rules, the chairman has to sign off on all subpoenas, unless that authority is delegated to someone else.
In an interview with Fox News a few days later, Nunes said he was still handling the portion of the committee's investigation related to whether Obama officials inappropriately requested the unmasking of the names of Trump campaign officials in intelligence documents.
Nunes and other Republicans have expressed concern that requests by Obama administration officials, like former national security adviser Susan Rice, to unmask members of the Trump campaign were politically motivated.
Those subpoenas were reportedly issued exclusively by Republican Rep. Devin Nunes, the committee chairman, with no input from Democrats.
"These officials said lawmakers submitted questions that intelligence officers could answer only by revealing the identities of USA individuals", according to the report. "I only learned about this late the night before, and that is a problem", he said.
"If he recused himself on subjects, Russia, then he shouldn't have access to documents relating to subject, Russia, and he shouldn't be issuing separate subpoenas attaching them to a bipartisan subpoenas that were issued this week", Pelosi said Friday.
"Nunes is not going to be able to go any further", the Democratic aide said, adding that, if he did, committee Democrats would pressure House Speaker Paul Ryan to remove Nunes as chairman.
Subpoenas were approved Wednesday for Flynn and his company, Flynn Intel Group, and Cohen, and his firm, Michael D. Cohen & Associates.
Nunes has been largely unseen in Washington since he recused himself from the probe, and the issuance of subpoenas is his highest profile action since stepping aside.
The staffer said the Democrats were informed that the unmasking subpoenas were being issued. Flynn plans to produce some of the documents by next week, said the person, who spoke on condition of anonymity to discuss Flynn's private interactions with the committee.