The Republican and Democratic leaders of the U.S. Senate Judiciary Committee asked Sessions and FBI Director James Comey on Wednesday to send the committee documents and provide a briefing on Flynn's resignation.
Citing reports that both the Federal Bureau of Investigation and Justice Department were involved in events leading to Flynn's departure, Senators Chuck Grassley and Dianne Feinstein said they raised "substantial questions" about Flynn's discussion with Russian officials.
Graham called for a broader bipartisan congressional investigation to be conducted by a newly formed special committee rather than existing committees, if it turns out Trump's presidential campaign communicated with the Russians.
But the top Republicans in the Senate and House of Representatives have insisted the matter be investigated by existing Republican-led committees.
The Senate and House Intelligence Committees and a subcommittee of the Senate Judiciary committee have announced they launched investigations into alleged Russian efforts to influence the election through computer hacking.
U.S. intelligence agencies previously concluded that Russia hacked and leaked Democratic emails during the presidential campaign as part of efforts to tilt the vote in the Nov. 8 election in Trump's favor.
Congressional inquiries into alleged Russian interference in the U.S. elections are gaining momentum as Capitol Hill investigators press intelligence and law enforcement agencies for access to classified documents.
The FBI and several U.S. intelligence agencies are investigating Russian espionage operations in the United States. They are also looking at contacts in Russia between Russian intelligence officers or others with ties to President Vladimir Putin's government and people connected to Trump or his campaign.
The FBI recently questioned Flynn about his telephone contacts with the Russian ambassador in Washington. People familiar with the agency's multiple probes said there was no evidence so far of pre-election collusion between Russians and Trump's campaign, or any evidence of criminal activity by Flynn or anyone else connected to Trump.
Some experts expressed concern the White House could curtail or divert probes into Flynn and Russian involvement in the election unless Congress becomes more aggressive by holding hearings and appointing an independent commission or special prosecutor into whether Trump's team violated federal laws in their contacts with Russia.
Intelligence agencies now overseen by Trump may not be ideally suited to the job, they added.
"It's not, at the end of the day, the job of the intelligence community to regulate the White House - and it shouldn't be," said Stephen Vladeck, a University of Texas law professor who focuses on constitutional law and national security.