President Donald Trump’s explosive accusations about his White House predecessor’s wiretapping activities during the 2016 election have dominated headlines since he first tweeted them Saturday morning -- and two top members of the Senate Intelligence Committee discussed their implications on CBS’ “Face the Nation.”

Sen. Mark Warner (D-Virginia) CBS News

Sen. Mark Warner (D-Virginia), the committee’s vice chair, said Mr. Trump’s Saturday morning tweets -- in which he accused former President Barack Obama of wiretapping Trump Tower for political reasons -- were “reckless.” Mr. Trump did not cite any evidence in his tweets, though similar claims had been circulating in the conservative media in recent days.

“I thought the president’s comments could no longer surprise me, but boy this one yesterday surprised me,” he said. “To make that type of claim without any evidence is I think very reckless.”

He said he was not aware of any FISA court order regarding Trump Tower, which the president said was under a wiretap in the lead-up to the 2016 election. Warner added that Mr. Trump’s tweets did suggest the president “doesn’t understand how you obtain a wiretap.”

“You have to go before a judge and show either probable cause, or if it’s in terms of foreign intelligence, a FISA court, and show that there is evidence of some type of contact with a foreign adversary,” Warner said.

Sen. Susan Collins (R-Maine) took a slightly more conciliatory tone toward the president’s wiretapping comments -- but said it “might be helpful” if he didn’t say anything else on the subject going forward.

“It would probably be helpful if he gave more information, but it also might be helpful if he just didn’t comment further and allowed us to do our work,” she said, noting that “at this point” she has seen “no evidence of what he’s alleged.”

Both Warner and Collins said they were confident the Intelligence Committee would get to the truth in a bipartisan, independent way. Warner pointed to the various ways Russia worked to interfere in the U.S. election -- including the hacking of the Democratic National Committee and internet trolls -- as well as Mr. Trump’s “unusual affection” for Russian President Vladimir Putin as reasons the investigation are so important.

“There’s nothing I’ve done in my life in public that’s as important as trying to getting this investigation done right and bipartisan, and get the facts out to the American people,” he said.

Collins said she is “convinced” the Senate Intelligence Committee will do “the kind of exhaustive, in-depth and prompt investigation that will help put these allegations to rest one way or another.”

Warner, asked whether the intelligence agencies were providing all the necessary information, said he has a “good working relationship” with FBI Director James Comey and that the committee will get “unprecedented” access.

“At this moment in time, you know, we’re at the beginnings of this,” he said. “We’re going to get the information we need to get to the bottom of this.”

With regard to Mr. Trump’s tax returns, which he has said are under audit and won’t be released until the audit is completed, Collins said it’s too soon to tell whether the Intelligence Committee will need them in order to fully complete its investigation into Russian ties -- but said senators will be prepared to ask for them if necessary.

“We’ll go wherever the evidence leads us and ... will get all of the information we need,” she said. “If that includes President Trump’s tax returns then I have confidence that we will ask for them. If we don’t need them in order to reach our conclusions then we won’t.”