Despite the finger-pointing aimed in his direction since Tuesday’s dismal GOP showing at the polls, President Trump is reportedly planning to go ahead with an announcement this week that he will seek the Republican presidential nomination in 2024.

Advisors to Mr. Trump say he has been dismissive of the criticism leveled at him and plans to go ahead with what one promised to be a “very professional, very buttoned up announcement” from his Mar-a-Lago estate on Tuesday.

A senior advisor on Mr. Trump’s 2016 and 2020 campaigns, Jason Miller, said on Steven Bannon’s podcast Friday that he spoke with the president and was told to relay the message that, “Of course I’m running. I’m going to do this, and I want to make sure people know that I’m fired up.”

While Mr. Trump has picked up endorsements from a few corners — Congresswoman Elise Stefanik of New York said in a statement over the weekend that she will “fully support him running again” — many in his party are saying he should step aside and let new blood take the GOP’s reins. Many others, however, have remained silent on the issue.

New Hampshire’s GOP governor, Chris Sununu, criticized the idea of the former president announcing before the holidays.

“So, now’s just a horrible time for big political statements — save that for early 2023 would be my message,” Mr. Sununu said Sunday on ABC’s “This Week.” “It’s going to be great for the media, ‘Saturday Night Live’ will probably love it, but for the rest of us, we’re going to focus on spending time with our families and kind of taking a breath in the quiet of a nonpolitical world.”

In an interview with a hometown newspaper, Congressman Mo Brooks of Alabama, an outspoken supporter of Mr. Trump’s in the 2020 campaign, said it would be a “bad mistake” for the party to nominate him to run for a third time.

“Donald Trump has proven himself to be dishonest, disloyal, incompetent, crude, and a lot of other things that alienate so many independents and Republicans,” Mr. Brooks reportedly told Al.com.

Pollster Frank Luntz, in an appearance on Fox News, expressed shock that Mr. Trump was going ahead with his announcement. “How do you announce when you had such a bad showing?” Mr. Luntz wondered, rattling off the list of Trump-endorsed candidates who lost on Election Day. “I don’t know how he announces. Maybe he just doesn’t get the message.”

A YouGov poll taken in the days since the midterm elections suggests a dramatic reversal in the status of Mr. Trump following Tuesday’s results. Only a month ago, more Republicans told the pollster that they preferred Mr. Trump at the top of the GOP ticket in 2024. Now, GOP voters say they would prefer Florida’s governor, Ron DeSantis.

Overall, 23 percent of those asked said they prefer Mr. DeSantis as the Republican nominee, and 20 percent said they prefer Mr. Trump. Even more, however, 41 percent, said they back neither man. Among Republican voters, 41 percent said they prefer Mr. DeSantis compared to 39 percent for Mr. Trump, while 8 percent said neither.

Apart from teasing his “big announcement” Tuesday, Mr. Trump has been relatively quiet on the topic on social media. With the exception of a note congratulating his daughter on her marriage Saturday, most of Mr. Trump’s public comments have focused on criticism of what he called the “rigged election” in states such as Arizona and Nevada where his preferred candidates lost.

On Sunday, Mr. Trump took to his last remaining social media platform and blamed Tuesday’s shellacking on the Senate minority leader, Mitch McConnell. “He blew the Midterms, and everyone despises him and his otherwise lovely wife, Coco Chow,” Mr. Trump wrote.

Mr. Trump has also taken potshots at the man many are holding up as the party’s preferred new standard-bearer following his decisive win on Tuesday — Florida’s Mr. DeSantis. In an appearance on the U.K.’s Sky News, however, Mr. Trump’s daughter-in-law, Lara Trump, said Mr. DeSantis should consider sitting out the 2024 race.

“I think that Ron DeSantis is very smart,” she said. “Look, he’s a young guy. There will be a lot of opportunities for him in the future — and he knows this — to run for president.”

“I can tell you, those primaries get very messy and very raw,” she added. “We’ve experienced that before. So wouldn’t it be nicer for him — and I think he knows this — to wait until 2028?”