Senator Lisa Murkowski, Republican of Alaska, said in an interview released on Sunday that she would not vote for former President Donald J. Trump. She also did not rule out the possibility of leaving the Republican Party.

In the interview, which Ms. Murkowski gave to CNN, she said that she would “absolutely” not support Mr. Trump in the general election in November. She said that she wished Republicans had nominated someone whom she could vote for, but that she “certainly can’t get behind Donald Trump.”

Asked whether she might leave the party and become an independent, she said that she considered herself “very independent-minded” and added, “I just regret that our party is seemingly becoming a party of Donald Trump.” But she did not give a yes-or-no answer, saying: “I am navigating my way through some very interesting political times. Let’s just leave it at that.”

If Ms. Murkowski left the Republican Party, it would be welcome news for Democrats facing a brutally difficult map in the Senate elections in November. Three of their current seats are up for election in red states, and several more are up for election in swing states. There are almost no opportunities to pick up seats currently held by Republicans, and there’s no room for error, given their very narrow majority.

Ms. Murkowski, who has served in the Senate for more than 20 years, has long been more moderate than many Republicans. Among other positions that are rare in her party, she supports abortion rights, and she has long been critical of Mr. Trump, including in voting to convict him in his impeachment trial after the Jan. 6, 2021, attack on the Capitol.

But most elected Republicans, even those who denounced Mr. Trump after Jan. 6, have fallen back in line behind him as it has become clear that he will be the party’s nominee for president.

Ms. Murkowski’s declaration that she will not vote for Mr. Trump puts her in the company of a small number of prominent anti-Trump Republicans, among them Senator Mitt Romney of Utah and former Representative Liz Cheney of Wyoming.

“No, no, no, absolutely not,” Mr. Romney said last month when asked by CNN whether he would vote for Mr. Trump.