A Pulitzer Prize winner resigned from the board of the Gerald R. Ford Presidential Foundation on Tuesday, protesting what he said was the group’s snub of former Representative Liz Cheney for its highest honor out of fears that Donald J. Trump would retaliate if he returned to the presidency.

David Hume Kennerly, an acclaimed photographer for his coverage of the Vietnam War, who was also the chief White House photographer for Mr. Ford, criticized the foundation for its decision to bypass Ms. Cheney for the Gerald R. Ford Medal of Distinguished Public Service.

In his resignation letter, which was obtained by The New York Times and first reported by Politico, Mr. Kennerly wrote that Ms. Cheney, one of Mr. Trump’s fiercest critics in the Republican Party, should have been a consensus pick for the honor for her role in the government’s response to the Jan. 6, 2021, attack on the U.S. Capitol. “America is fortunate to have Liz Cheney still out there on the front lines of freedom vigorously defending our Constitution and democratic way of life,” he wrote.

Mr. Kennerly, who worked for United Press International and had been a board member since the early 2000s, nominated Ms. Cheney for the medal last year and said that he had urged the foundation’s executive committee to reconsider her this year. He noted that Ms. Cheney was a board member of the foundation.

“A key reason Liz’s nomination was turned down was your agita about what might happen if the former president is re-elected,” Mr. Kennerly wrote. “Some of you raised the specter of being attacked by the Internal Revenue Service and losing the foundation’s tax-exempt status as retribution for selecting Liz for the award.”

Gleaves Whitney, the executive director of the Ford Presidential Foundation, gave a different reason in a statement about why Ms. Cheney was passed over by the organization: that her name was being bandied about for a potential third-party candidacy for president.

“At the time the award was being discussed, it was being publicly reported that Cheney was under active consideration for a presidential run by No Labels,” Mr. Whitney said, referring to a centrist political group. “Exercising its fiduciary responsibility, the executive committee concluded that giving the Ford medal to Cheney in the 2024 election cycle might be construed as a political statement and thus expose the foundation to the legal risk of losing its nonprofit status with the I.R.S.”

No Labels last week abandoned its plans to run a presidential ticket in the 2024 election after its recruitment of high-profile candidates fizzled.

No Labels’ chief strategist, Ryan Clancy, said in a statement on Wednesday that the group had briefed Ms. Cheney on its 2024 ballot access strategy but that she declined to be involved out of concern it could help the electoral prospects of Mr. Trump. He added that No Labels did not make an offer to Ms. Cheney to appear on its ticket.

Ms. Cheney did not immediately respond to requests for comment left with a spokesman on Wednesday.

The top Republican on the special House committee that investigated the Jan. 6 attack, Ms. Cheney has regularly been vilified by Mr. Trump and his supporters. Her criticism and defiance of the former president led to her ouster during the Republican primary in 2022 in her House district in Wyoming, which she represented for six years in Congress.

A spokesman for the Trump campaign did not immediately respond to a request for comment on Wednesday.

Ms. Cheney’s father, former Vice President Dick Cheney, was a White House chief of staff for Mr. Ford and is listed on the foundation’s website as a trustee.

Mr. Kennerly accused those who rejected Ms. Cheney for the honor of pandering to Mr. Trump, the presumptive Republican presidential nominee, and said that Mr. Ford, the medal’s namesake, would not have acquiesced.

“Those of you who rejected Liz join many ‘good Republicans’ now aiding and abetting our 45th president by ignoring the genuine menace he presents to our country,” Mr. Kennerly wrote, adding, “Gerald Ford wouldn’t have been intimidated by phantom consequences.”