Yet again, it was Mr. Trump dominating the news.

Fox News aggressively reported the search, featuring overhead camera shots from above Mar-a-Lago and multiple interviews with Trump family members, including his son Eric and daughter-in-law, Lara, and former administration officials, such as Stephen Miller, his chief policy adviser, and Stephen K. Bannon, the chief strategist.

“A dark day for our republic,” Sean Hannity, a Fox News host, said to open his prime-time show on Monday night. “The Department of Justice, the rule of law, what looks to be potentially a shocking overreach — we’ll find out in due time — that will have serious ramifications potentially for many, many years to come.”

With right-wing media amplifying the fury directed at the Biden administration, the wide-ranging show of unity was the latest sign of Mr. Trump’s exhaustive reordering of the Republican Party, which he has transformed largely into a promotional vehicle for his own political brand.

The significance of the intense loyalty he has exacted from Republicans was reflected in Mr. Trump’s calculations on Tuesday that a search of his home by federal investigators would have positive repercussions inside his party. Meeting with advisers Tuesday, Mr. Trump was angered by the F.B.I.’s search but insisted it would help him politically, according to one. Still, he dismissed a push from some of his advisers to fly back to Mar-a-Lago and immediately announce a new presidential campaign, according to two people familiar with the discussions.

Other allies of Mr. Trump argued for a “Draft Trump” effort, an idea Senator Lindsey Graham of South Carolina had floated shortly after Mr. Trump left office, a person familiar with the discussions said.

Mr. Trump is weighing an increasingly likely third bid for the White House, which could come in an unusually early announcement in part to try to shield himself from a stream of damaging revelations from investigations into his actions before and after the 2020 election.