Feinstein, the Senate Judiciary Committee's top Democrat, said on CNN's "State of the Union" that she would discuss bringing Sessions before her panel with the committee's Republican chairman, Iowa Sen. Chuck Grassley.
"I think he should come back and clarify it," Feinstein said of Sessions.
Last Monday, unsealed court records showed former Trump campaign adviser George Papadopoulos pleaded guilty
to making false statements to the FBI about his interactions with foreign officials close to the Russian government -- the campaign's clearest connection so far to Russia's efforts to meddle in the 2016 election.
According to the court documents, Papadopoulos suggested at a campaign meeting that then-candidate Donald Trump and Russian President Vladimir Putin meet. A photo showed Sessions also attended that campaign meeting, and a source told CNN
that at the meeting, Sessions vetoed the proposed Trump-Putin sit-down.
Trump himself did not dismiss the idea.
"He didn't say yes and he didn't say no," the official said, declining to be more specific about Trump's response to Papadopoulos.
The latest revelations have increased scrutiny
on Sessions, who previously came under fire for saying during his Senate confirmation hearing that he had no interactions with the Russians only to be later corrected that he met with Sergey Kislyak during the campaign, who was the Russian ambassador to the US at the time. After the reports, Sessions went on to recuse himself
from investigations related to the 2016 campaign.
In her interview Sunday, Feinstein praised Minnesota Democratic Sen. Al Franken, who originally asked Sessions about Russian communications, and noted Franken had already called
for Sessions to provide more testimony.
Feinstein did not give her opinion on whether Sessions was being deliberately untruthful.
"I'm not going to say whether it was a lie or not," Feinstein said.
Feinstein, who is also a member of the Senate Intelligence Committee, said she had not seen any evidence that any "dirt" regarding emails linked to Hillary Clinton, which court records said Papadopoulos discussed with a foreign contact close to the Russian government, was given to the Trump campaign. She added that she also has not seen communications that the campaign wanted the information released through different means, such as through WikiLeaks.
Speaking on CBS's "Face the Nation," Senate intelligence committee ranking Democrat Mark Warner, of Virginia, said he might want to hear more from Sessions.
"Listen, I want to give the attorney general the benefit of the doubt, but a picture's worth a thousand words," Warner said. "The fact that Mr. Papadopoulos was there with that meeting with, with then Senator Sessions, if, if there's more information that he needs to clarify, we'd like to hear that."