Committee chairman Sen. Richard Burr of North Carolina and Virginia Sen. Mark Warner, the top Democrat on the committee, said at a joint news conference Tuesday they were seeking a briefing from the White House on what was said last week between Trump
and Russian Foreign Minister Sergey Lavrov and Russian Ambassador to the US Sergey Kislyak.
"Once Mark and I have an opportunity to talk individuals that were in the meeting, that will either confirm our confidence or possibly shake our confidence," Burr said.
Warner added that if transcripts of the meeting exist, the committee would be seeking those, too.
"We're trying to go the extra mile -- we owe the White House the chance to present us with the information, present us with the truth," Warner said. "We want to know from people in the room, also want to know if there are these supposed transcripts."
The intelligence committee met Tuesday afternoon in a previously scheduled closed session, a meeting that Burr and other senators said did not address Trump's meeting with Russian officials.
The reports prompted Minority Leader Chuck Schumer and other lawmakers -- including several Republicans -- to call for the White House to provide the Senate panel with any transcripts of the meeting.
"If it is in fact true that info was shared with the Russian ambassador, then it seems to me it should be OK to share with US senators," Republican Sen. Thom Tillis of North Carolina told reporters.
Burr declined to weigh in on the specifics of the disclosures beyond saying that the President has the ability to share intelligence -- to a point.
"This is probably a good time to take a breath, and understand the President has the ability and the right to talk about intelligence," he said. "There is a point that you cut that off with foreign leaders, especially when sources and methods are involved, so it's crucial that we talk to individuals to find out exactly what was said not necessarily what was not said."
Burr said he was hoping to get some answers from the White House by the end of the day.
He declined to address reports Tuesday that Israel was the source of some of the information that Trump shared with the Russians. On the House side, CIA Director Mike Pompeo is expected to brief that chamber's intelligence committee
on Tuesday on Trump's apparent leaking.
Trump defended himself in a series of tweets Tuesday, saying he had the "absolute right" to share information about terrorism threats with the Russians, but his message notably lacked any reference to whether the information is classified.