The political action committee of former Representative Liz Cheney began broadcasting an attack on Donald J. Trump’s fitness for office on Tuesday in the key state of New Hampshire, using her narration to accuse the former president of the greatest “dereliction of duty” in American presidential history.

It is unclear whether the advertisement by Ms. Cheney’s leadership PAC, The Great Task, is another hint that she may run for president or a stand-alone effort to soften Mr. Trump’s support in the state that will hold the first Republican primary in February.

But at this political moment, when Mr. Trump’s rivals for the Republican presidential nomination in 2024 have been reluctant to attack the front-runner, Ms. Cheney has fired an opening salvo, demanding that Republican voters rebuff the former president’s effort to return to power.

In the ad, which includes graphic and violent footage of his supporters at the Jan. 6, 2021, attack on the Capitol, Ms. Cheney says Mr. Trump refused to accept his re-election defeat. When all his efforts to cling to power failed, she says, “he mobilized a mob to come to Washington and march on the Capitol.”

“Then he watched on television while the mob attacked law enforcement, invaded the Capitol and hunted the vice president,” she said.

Ms. Cheney also warned:“Donald Trump is a risk America can never take again.”.

Steven Cheung, a spokesman for Mr. Trump’s presidential campaign, responded by calling Ms. Cheney “a stone-cold loser who is now trying to grift her way to relevance.”

Ms. Cheney hinted that she would return to politics after a crushing primary defeat in August by a pro-Trump Republican challenger, Harriet Hageman, who jettisoned her from the House seat in Wyoming she held for three terms. The daughter of former Vice President Dick Cheney, Ms. Cheney was once considered a potential speaker of the House. But her own party conference banished her from her senior Republican leadership post over her stalwart opposition to Mr. Trump after the Jan. 6 attack. She went on to become one of two Republicans who served on the House committee that investigated the riot at the Capitol.

Her party and its core voters remain implacably opposed to her position on Mr. Trump, as evidenced by the former president’s commanding lead in party presidential polling. Those same polls have consistently put the party’s support for her at around 2 percent.