Former Obama national security adviser Susan E. Rice said Tuesday that she “absolutely” never sought to uncover “for political purposes” the names of Trump campaign or transition officials concealed in intelligence intercepts, and she called suggestions that she leaked those identities “completely false.”

“I leaked nothing, to nobody, and never have and never would,” Rice said in response to the latest charges and countercharges flowing from politically charged investigations into Russian interference in the presidential election.

Since they first surfaced over the weekend, the Rice reports have quickly overtaken the steady drumbeat of revelations about connections to Moscow that have dogged President Trump for months. On Tuesday, the subject dominated cable news and flooded Twitter.

“RICE ORDERED SPY DOCS ON TRUMP?” the President retweeted, with a link to the Daily Caller and a Drudge Report headlined “Boiled Rice.”

A number of Republican lawmakers said that Rice should be called to testify before congressional inquiries into what US intelligence has said were Russian efforts not only to roil the presidential race, but also to tip the scales in Trump’s favour.

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“If the reports are right, then she will be of interest to us,” said Sen. Richard Burr (R-NC), chairman of the Senate Intelligence Committee, which, along with its House counterpart and the FBI, is investigating the matter.

“When it comes to Susan E. Rice, you need to verify, not trust,” Sen. Lindsey O. Graham (R-SC) said in an interview with 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. Tom Cotton (R-Arkansas), called Rice the “Typhoid Mary of the Obama administration.”

Beyond Trump’s tweets, however, the White House was uncharacteristically restrained on the subject, as its media and Capitol Hill allies expressed outrage on its behalf. “It’s not for me to decide who should testify or how they should do it,” press secretary Sean Spicer said.

Rep. Adam B. Schiff (California), the ranking Democrat on the House Intelligence Committee, called the attention focused on Rice a diversionary tactic. He has also called on the Intelligence Committee’s chairman, Rep. Devin Nunes (R), a Trump transition official and fellow Californian, to recuse himself from the investigation. The White House, Schiff said, has a “strong desire... that we lose our focus, that we not pursue the investigation of Russia, particularly as it might impact the Trump campaign.”

At the same time, Schiff told CNN, Rice has long been a target of what he called the “Breitbart crowd . . . the hard right” since the September 2012 attacks on a US diplomatic facility in Benghazi, Libya. Four US officials were killed in an extremist attack that Rice initially described as an anti-American protest that evolved into violence.

White House chief strategist Stephen K. Bannon is the former chairman of Breitbart News, which he has described as “the platform for the alt-right,” an anti-globalist movement that seeks a whites-only state.

Asked Tuesday whether she was willing to testify, Rice told MSNBC, “Let’s see what comes.” Investigations on “Russian involvement in our electoral process are very important, they’re very serious, and every American ought to have an interest in those investigations going wherever the evidence indicates they should,” she said.

“I have an interest as an American citizen, as a former official,” Rice said. “I would want to be helpful in that process if I could.”

The focus on Rice comes as lawmakers are trying to iron out why Nunes went to the White House two weeks ago to view documents that he later said suggested that the names of Trump transition team members had been improperly “unmasked.” Top officials can ask intelligence agencies to reveal the names to them for national security or other reasons.

The term refers to revealing a name that has been blacked out in an intelligence surveillance report. The law does not permit surveillance of US people without a warrant; if one shows up in authorised surveillance of a foreign person, it is “masked.”

News media reports on contacts between Russia and Trump associates, including in The Washington Post, have included names said to have appeared in intelligence reports — either persons named in conversations between foreigners, or conversations directly between foreigners and US persons.

Most prominent among them is former Trump national security adviser Michael Flynn, whose ­December phone conversations with Russia’s ambassador in Washington included references to US sanctions imposed under President Barack Obama. After a Post report on the conversations, Trump ousted Flynn for mischaracterising them to Vice President Pence.

Trump later charged that he, himself, had been surveilled under orders from Obama, who allegedly was seeking to undermine him. The administration has said repeatedly that attention should be focused on who unmasked and leaked, rather than on the information revealed.

After Nunes’s statement about the unmasking, The Post reported last week that at least three White House officials were involved in handling the files shown to him. On Monday, a report by Bloomberg View suggested that those officials began examining the files after discovering that Rice, while working as Obama’s national security adviser, had requested the names be unmasked.

The Daily Caller followed with a report, sourced to former US attorney Joe DiGenova and “other official sources,” that said that Rice ordered US spy agencies to produce “detailed spreadsheets” of phone calls involving Trump and his aides.

The White House immediately drew attention to a PBS interview in which Rice, on the same day as Nunes’s statement about the documents, said, “I know nothing about this.”

Speaking Tuesday to MSNBC, Rice said that she, like other top officials in all administrations, sometimes asked for names of US persons that had been blacked out in intelligence reports — “on every topic under the sun when it seemed relevant” — when necessary to “protect the American people and do our jobs.”

“Let me give you an example — completely made up,” she said. “Let’s say there was a conversation between two foreigners about a conversation they were having about an American who was proposing to sell to them high-tech bomb-making equipment.

“Now, if that came to me as the national security adviser, it would matter enormously — is that some kook sitting in his living room communicating via the Internet to sell something he doesn’t have, or is this a serious person or company or entity with the ability to provide this technology perhaps to an adversary? That would be an example of how it is necessary knowing who that person was to assess that information.”

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“I can’t say that the pace of unmasking requests” rose during the Trump transition, Rice said. But, she said, “the pace of intelligence reports on Russian interference efforts increased” beginning in late summer. Intelligence officials went back to rescrub the reports after Obama requested a compilation of them, which was delivered in January, she said.

“There was no spreadsheet, nothing of the sort,” Rice said.

“The allegation is that somehow Obama administration officials utilised intelligence for political purposes,” she said. “Absolutely false.”