Another member of the Washington political media stepped forward Thursday to claim he was threatened by the Obama White House, shortly after the White House denied reports that an adviser threatened famed Watergate journalist Bob Woodward.

The latest claim comes from Lanny Davis, who served as counsel to former President Bill Clinton and later went on to write a column for The Washington Times. In a radio interview on WMAL, Davis said that a "senior Obama White House official" once called his editor at the Times and said that if the paper continued to run his columns, "his reporters would lose their credentials."

Davis said he "couldn't imagine why this call was made" since he's an Obama supporter.

But he called the alleged threat "unfortunate."

The account comes after Woodward claimed Wednesday night that a White House aide sent him an email saying he would "regret" his recent reporting on the sequester battle. The aide was not identified, but an official familiar with the exchange told Fox News it was National Economic Council Director Gene Sperling -- the tone of the email was rather mixed, as it also included an apology. That was after Woodward wrote a column this past weekend claiming Obama was trying to re-write history -- regarding not only whose idea the sequester was, but also how it would take effect.

Woodward wrote that based on his reporting earlier in the budget battle, the president was trying to move the goalposts by trying to replace the sequester with a mix of tax hikes and spending cuts -- instead of solely spending cuts.

After Politico reported late Wednesday that Woodward was coming forward to claim he was threatened, a White House aide denied the claim.

"Of course no threat was intended," wrote the White House aide. "As Mr. Woodward noted, the email from the aide was sent to apologize for voices being raised in their previous conversation. The note suggested that Mr. Woodward would regret the observation he made regarding the sequester because that observation was inaccurate, nothing more. And Mr. Woodward responded to this aide's email in a friendly manner."

White House Press Secretary Jay Carney said Thursday that Woodward and Obama's advisers merely "had a factual disagreement that I think we stand by."

He stressed that it's clear nobody was threatening anybody, and that the tone was "respectful."

According to Politico, Woodward said he was "yelled at" by an Obama aide over his weekend column in the Post. Then, he said he received a page-long email from the aide -- apparently Sperling -- that said: "I apologize for raising my voice in our conversation today. ... You're focusing on a few specific trees that give a very wrong impression of the forest. But perhaps we will just not see eye to eye here. ... I think you will regret staking out that claim."

Animosity between Woodward and the Obama team is rising, as the journalist has repeatedly needled the administration on its sequester talking points. His reporting bolstered claims that the sequester idea originated at the White House. And this week, he called the administration's handling of the cuts "madness."

Former Obama adviser David Plouffe tweeted Wednesday: "Watching Woodward last 2 days is like imagining my idol Mike Schmidt facing live pitching again. Perfection gained once is rarely repeated."

Fox News' Ed Henry contributed to this report.