The president said, "Thank you very much, no", shaking his head.
He appeared to respond again: "No".
She said the threat to the United States electoral system "still exists, which is why we are taking steps to prevent it".
"It's imperative we get to the bottom of what is going on so we can be prepared to protect ourselves in advance of the 2018 elections", Graham said.
Later, Ms Vega tweeted that the president had been looking directly at her when he answered.
But I'm telling you today, I trust USA intelligence.
Former Director of National Intelligence James Clapper confirmed Thursday that Donald Trump was briefed on USA intelligence findings that Russian President Vladimir Putin personally ordered cyberattacks to attempt to sway the 2016 presidential election. "He does believe that they would target US elections again".
He told a congressional committee in February he had already seen evidence that Russian Federation was targeting the upcoming mid-term elections in November.
He notably flip-flopped repeatedly over what exactly he said to Mr Putin at the summit, and whether he believes Russian Federation meddled in the 2016 election campaign on Mr Trump's behalf.
House Minority Leader Nancy Pelosi said Trump has done "deep damage" to the country.
On Wednesday, Trump criticized Clapper, who was appointed as DNI chief by President Barack Obama, as someone in whom he has "no confidence" during an interview with CBS News. "It's called Trump Derangement Syndrome!"
Syrian forces seize village in southwest, widening offensive - monitor
In April previous year , thousands of people were shuttled out of the two villages to government territory in an agreement. Israel's Defence Minister Avigdor Lieberman stated last month that, "We are closely monitoring events in southern Syria".
Mr Trump, by contrast, has come under widespread domestic criticism about the meeting both from Democratic opponents and senior Republicans.
Some 71% of Republicans polled approved of his response to Russian Federation, while only 14% of Democrats were in favour.
"Well, I would, because he's in charge of the country", Trump said when asked if he holds him responsible for the interference.
Secretary of State Mike Pompeo is due to testify before the Senate next week about the summit.
So what did he say to Putin about it, then?
Democrats and some members of Trump's own Republican Party have criticized him for accepting at face value Putin's denial that Russian Federation interfered in the vote.
Senator Jeff Flake, a Republican and a vocal critic of Trump, had labelled his performance as "shameful".
"The president must appreciate that Russian Federation is not our ally", Ryan said.
Though Trump didn't mention Browder by name or endorse a swap that involved him, he did praise Putin's idea as "an incredible offer".
Clapper has frequently criticized Trump's behavior toward Russian Federation, including in his news conference Monday with Putin in Helsinki, Finland. I blew it yesterday, but I blew it because I didn't want to insult the guy that I just had a fantastic conversation with, and I think we could accomplish great things together.
Trump continued, "You know, Russian Federation and the United States control 90 percent of the nuclear weapons in the world and getting along with Russia-and not only for that reason-it's a good thing, not a bad thing".
U.S. Sen. Marco Rubio (R-Fla.), who took the president at his word Tuesday, said yesterday there was no question that Russian Federation continues efforts to interfere with U.S. elections systems - saying it was a "guarantee".