Mr. Trump’s achievement also drew a rebuke of sorts from the last two Republican presidents. Aides to former Presidents George Bush and George W. Bush said they would not participate in or comment on the presidential campaign. By contrast, they supported the Republican nominees in the last two elections: John McCain in 2008 and Mitt Romney in 2012. Mr. Trump ran a sharply negative campaign against former Gov. Jeb Bush of Florida, the son of the elder Mr. Bush and brother of the younger, who dropped out in February.

For some in the party, the question of whether to embrace Mr. Trump is not merely an intellectual exercise. Some staff members at the Republican National Committee were told Wednesday that if they were unable to get behind the nominee, they should leave by the end of the week.

Representative Peter T. King of New York, whose Long Island district Mr. Trump won overwhelmingly in the April 19 primary, echoed other Republicans in pledging to vote for Mr. Trump even though he had reservations, calling Mr. Trump “a guy with no knowledge of what’s going on.”

“As far as any involvement or campaigning, it’s really going to depend on him filling in the gaps and consolidating his policies,” Mr. King said. “Right now, there’s no real coherence.”

The lingering resistance to Mr. Trump is especially strong in some of the states and congressional districts with hotly contested races this year. Representative Carlos Curbelo, who is from a competitive district in South Florida and has been outspoken about his refusal to support Mr. Trump, said Hispanics in his district were furious at Mr. Trump over his inflammatory language about Latinos.

“Resentment is a kind way of putting it,” Mr. Curbelo said. “People are offended and really incredulous.” He added that he would consider supporting a third-party presidential candidate, though that option did not appear to have much support among other Republicans on Wednesday.

But the widespread discomfort and anxiety about Mr. Trump was utterly clear in the hours after he became the presumptive nominee on Tuesday night. Most leading Republicans were publicly silent. And the dearth of congratulatory news releases and Twitter posts spoke volumes.