Former National Security Adviser Susan E. Rice categorically denied Tuesday that she did anything wrong by unmasking the identities of Trump campaign officials swept up in U.S. surveillance, while the Republican chairman of a Senate probe into Russian meddling in the 2016 election said his panel may want her to testify.

Ms. Rice did not explicitly deny having requested that names be added to raw surveillance intelligence relating to Trump associates. But she pushed back hard against insinuations that her actions were politically motivated or tied to any organized scheme to compile dirt on the Trump campaign.

“The allegation is that somehow Obama administration officials utilized intelligence for political purposes,” she said in an interview on MSNBC. “That is absolutely false.”

Her comments came a day after The Washington Times and others verified a Bloomberg View report that Ms. Rice had requested the “unmasking” — the identification of Americans whose names would have otherwise been redacted in intelligence reports — of Trump officials on dozens of occasions.

The revelation has added a fresh twist to an increasingly heated debate in Washington over the extent to which the Obama administration’s handling of classified information should become the focus of congressional probes into Russian meddling in last year’s election.

Senate Intelligence Committee Chairman Richard Burr indicated Tuesday that he may want to hear more details from Ms. Rice. “The committee will follow the facts where they lead,” a spokesman for the North Carolina Republican said, as pressure mounted from other influential GOP lawmakers to call for Ms. Rice to testify under oath.

“When it comes to Susan Rice, you need to verify, not trust,” Sen. Lindsey Graham told Fox News on Tuesday. “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.”

Ms. Rice, who also served as the Obama administration’s U.N. ambassador, has a reputation across Washington as tough, combative figure. Pundits noted that her interview on Tuesday resembled a rhetorical dance, as she seemed at points to imply that she had, indeed, requested the identities of blacked-out Trump team names in the intelligence reports.

“There were occasions when I would receive a report in which a U.S. person was referred to, name not provided,” Ms. Rice told host Andrea Mitchell. “Sometimes in that context in order to understand the significance of the report and assess its significance, it was necessary to request the information as to who that person was.”

To protect national security, Ms. Rice said, her job often required her to learn the identity of masked U.S. officials. She added that while there was a spike in raw intelligence collection during the election, she said she didn’t recall a significant increase in unmasking during that time.

The Trump administration cast doubt on her statements Tuesday.

White House Press Secretary Sean Spicer declined to speculate on whether Ms. Rice should be called for congressional testimony, but argued that her comments seemed contradictory.

Mr. Spicer pointed to an appearance Ms. Rice had made on PBS “Newshour” last month, during which she fielded questions about House Intelligence Committee Republican chairman Rep. Devin Nunes’ revelation that Trump associates had been incidentally swept up in U.S. surveillance of foreign targets and unmasked.

“She was the one who went out and said, quote, that she had nothing to do with this on a program a few weeks ago,” Mr. Spicer said. “Now you see more and more reports.”

By day’s end Tuesday, the fast-paced story around the Russian meddling and intelligence probes had spun off in an entirely different direction, with the House Intelligence Committee’s top Democrat saying that President Trump had actually praised his work last week at the White House.

In an interview with Yahoo News, Rep. Adam Schiff said, “The president began the meeting last Friday by saying, ‘So, are you getting to see everything you wanted?’ And I said, ‘Actually, no — we have this issue,’ and I described what it was, and he said, ‘Well I’m fine with your staff seeing the documents — I have no problem with that.’”

The documents Mr. Trump referred to are the same documents Mr. Nunes had earlier seen, and the same documents Ms. Rice is now in the spotlight over.

• Tom Howell contributed to this report.

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