Former US presidents George H W Bush and George W Bush will not endorse Donald Trump's candidacy for president, aides have told local media.
And the highest ranking Republican, Paul Ryan, said he cannot currently support the presumptive Republican nominee.
This marks a first for the 91-year-old former president George H W Bush, who had endorsed Republicans in the past five elections.
United States House Speaker Mr Ryan said Mr Trump needed to strive for "higher aspirations", and, although Mr Trump "deserved" the nomination, he must do more to unite the party.
There has been persistent speculation that Mr Ryan, the 2012 vice-presidential nominee alongside Mitt Romney, may make a last-minute run for the top job, but he has frequently sought to dispel those claims, and did so again on Thursday (local time).
"I think what a lot of Republicans want to see is that we have a standard bearer that bears our standards," Mr Ryan told CNN.
Mr Trump's remaining opponents dropped out earlier this week leaving him as the presumptive Republican nominee.
Both Bush men had previously campaigned this year for former Florida Governor Jeb Bush, who exited the race in February.
They had each supported past Republican presidential nominees John McCain in 2008 and Mitt Romney in 2012.
Although neither former president has openly attacked Mr Trump or his policy proposals, George W Bush made a veiled criticism at a campaign event for his younger brother in February saying, "the strongest person usually isn't the loudest one in the room".
"I understand that Americans are angry and frustrated. But we do not need someone in the Oval Office who mirrors and inflames our anger and frustration," George W Bush told the South Carolina audience.
Many Republican candidates for lower offices are concerned about running on the same ballot as Donald Trump, who has alienated minority voters through his rhetoric about building a wall with Mexico and banning US entry to Muslim travellers.
Many Americans choose to vote for either the Democrat or Republican Party, rather than weighing the individual candidates, and Republican representatives fear that voters who oppose Mr Trump may eschew the Republican Party all together.
Mr McCain, who is running for his sixth term as senator for the state of Arizona, privately told donors that he will face a tough re-election campaign sharing a ballot with Trump.
"If Donald Trump is at the top of the ticket, here in Arizona, with over 30 percent of the vote being the Hispanic vote, no doubt that this may be the race of my life," the former candidate said, according to audio obtained by Politico on Thursday.
Previous Republican nominees for president, Mr McCain and Mr Romney, have both said they would not attend the Republican National Convention in July.
Hours after Mr Trump's remaining rivals dropped out, the Democrat frontrunner Hillary Clinton released a campaign ad seeking to take advantage of the vitriolic language and insults that other Republicans have used to refer to Mr Trump.
In her tweet to share the video, Mrs Clinton wrote "Republicans agree: Donald Trump is reckless, dangerous, and divisive."
Republicans agree: Donald Trump is reckless, dangerous, and divisive. https://t.co/fUkISvxMmc— Hillary Clinton (@HillaryClinton) May 5, 2016
Some Republicans, including a former top adviser and speechwriter to Senator McCain, have begun to openly call for the party to oppose the presumptive nominee and to work to independently elect a conservative candidate, such as Nebraska Senator Ben Sasse, who has indicated that he will not be supporting Mr Trump.
In a series of media interviews following Mr Trump's emergence as the sole remaining Republican candidate, he described his vision for the first 100 days of his administration.
He said within the first 100 days, a wall on the US-Mexico border will be designed, a ban on Muslims will be in place, and plans to revoke President Obama's executive orders will be under way.
"I know people aren't sure right now what a President Trump will be like," he told the New York Times on Wednesday. "But things will be fine. I'm not running for president to make things unstable for the country."
Top Republicans are divided over supporting Mr Trump.
- New Hampshire Senator Kelly Ayotte
- Retired neurosurgeon Ben Carson
- New Jersey Governor Chris Christie
- Former Louisiana Governor Bobby Jindal
- Senator Majority Leader Mitch McConnell
- Nevada Governor Brian Sandoval
- Wisconsin Governor Scott Walker
- House Speaker Paul Ryan
- Former President George H W Bush
- Former President George W Bush
- Former Massachusetts Governor Mitt Romney
- Nebraska Senator Ben Sasse
Yet to comment:
- Former Florida Governor Jeb Bush
- Texas Senator Ted Cruz
- Ohio Governor John Kasich
- Florida Senator Marco Rubio