(Jenny Starrs/The Washington Post)

The Senate Intelligence Committee chairman is not ruling out interviewing former national security adviser Susan Rice over allegations that she sought to have the identities of President Trump’s transition team revealed in foreign surveillance reports.

“If the reports are right,” Chairman Richard Burr (R-N.C.) said on Tuesday, “then she will be of interest to us.”

Some Republican lawmakers have been clamoring for the Senate Intelligence Committee to force Rice to testify under oath after a report from Bloomberg’s Eli Lake suggested Rice on dozens of occasions requested the identities of people connected to Trump be “unmasked.”

“When it comes to Susan Rice, you need to verify, not trust,” Sen. Lindsey O. Graham (R-S.C.) said Tuesday during an interview on Fox News. “I think every American should know whether or not the national security adviser to President Obama was involved in unmasking Trump transition figures for political purposes.”

Sen. John McCain (R-Ariz.), who has been extremely critical of the Trump administration’s openness to a thaw with Russia, also said that the Rice situation “obviously, it needs to be investigated.”

Then-national security adviser Susan Rice is seen on the South Lawn of the White House in July 2016. Rice says it's “absolutely false” that the previous administration used intelligence about President Trump's associates for political purposes. (Carolyn Kaster/AP)

But he warned against drawing premature conclusions — and also said that the names of other officials would pop up before the investigation is completed.

“I promise you there will be many more,” he stated.

Rice has denied the allegations, calling them “absolutely false” in an MSNBC interview on Tuesday.

The focus on Rice comes as lawmakers are trying to iron out why House Intelligence Committee Chairman Devin Nunes (R-Calif.) went to the White House grounds two weeks ago to view documents that he says suggest members of the Trump transition team’s identities were potentially improperly unmasked. A Washington Post report found that at least three White House officials are tied to the files that were shared with Nunes, while the Bloomberg report suggests that those officials began handling the files after they discovered Rice’s requests to unmask certain people’s identities.

Nunes would not comment Monday night on whether Rice was in any way associated with the documents he had seen.

But Republicans have long been suspicious of Rice, who emerged as a central figure in the party’s long probe of what led to the deaths of four Americans in Benghazi, Libya, in 2012.

“Susan Rice is the Typhoid Mary of the Obama administration foreign policy. Every time something went wrong, she seemed to turn up in the middle of it,” Sen. Tom Cotton (R-Ark.), a member of the Senate Intelligence Committee, said Tuesday on Hugh Hewitt’s radio program.

He also said there was “no doubt” that Rice should be the subject of a committee hearing, pledging that the Intelligence Committee “ought to review...and will review” both Rice’s alleged actions and questions raised by Nunes’s claims.

As national security adviser, Rice had the authority to request to see the identities of names that otherwise would have been obscured in surveillance reports. That authority applied to situations where knowing the identity of a person contained in the report was necessary for understanding its intelligence value.

Rice said on MSNBC Tuesday that that was the only context in which she ever requested the “unmasking” of any names – “absolutely not for any political purposes, to spy, expose, anything.”

She also denied being the source of any leaks — another area of focus for Congress as it probes the extent of the Trump team’s ties to Russian officials.

Burr has repeatedly promised that his Intelligence Committee will follow the facts surrounding Russia’s suspected interference in the 2016 elections wherever they lead. This week, the panel embarked on 20 interviews, most of them with members of the intelligence community that played a role in compiling a January assessment determining that Russia had tried to interfere in the 2016 elections with the purpose of helping Trump.

In the House Intelligence Committee, a similar probe all but ran aground last week, as Democrats accused Nunes of going around the committee to coordinate with the White House on the surveillance reports and alter the roster of witnesses testifying before the panel.

Nunes, like many others Republicans, has focused on the leaks of information alleging ties between the Kremlin and the Trump team, calling them the only clearly criminal act that took place and stressing there is no evidence of collusion between Trump allies and Russian officials. Democrats, however, have accused Nunes of effectively facilitating improper leaking himself when he went to the White House to view the information he then referred to publicly.

After a week and a half of wrangling, committee ranking member Adam Schiff (D-Calif.) also went to the White House Friday to view those documents. He said in a statement that the materials would soon be made available to the entire committee.

But House Democrats and Republicans are still at odds over how their investigation can proceed.

Nunes cancelled a public hearing for last week with former director of national intelligence James R. Clapper, former CIA director John Brennan, and former acting attorney general Sally Yates. The Washington Post reported that the administration sought to prevent Yates’s testimony, but Nunes maintained the hearing was cancelled to allow committee investigators to again grill FBI Director James B. Comey and NSA Director Adm. Mike Rogers.

Nunes said in an interview Monday evening that the committee might resume certain interviews later this month, as soon as the third week of April. But he stressed there were still some witnesses whose testimony would have to wait until after Comey and Rogers return. Nunes said that Comey was the one holding tup hat briefing; a spokesperson for the FBI said Tuesday that the agency was “continuing to work with the committee on its requests.”