Mitt Romney has secured a key endorsement for his presidential bid from former Florida Governor Jeb Bush.
Mr Bush, whose support comes the day after Mr Romney secured a clear victory in
Illinois,called on Republicans to "unite" behind the Romney campaign.
Correspondents say the backing of the respected Republican suggests the party establishment could be coalescing around Mr Romney.
The eventual nominee will challenge Barack Obama in November's election.
The next primary will be held in Louisiana on Saturday, with more votes due in Wisconsin, Maryland and the District of Columbia on 3 April.
"Primary elections have been held in 34 states, and now is the time for Republicans to unite behind Governor Romney and take our message of fiscal conservatism and job creation to all voters this fall," Mr Bush said in a statement.
"I am endorsing Mitt Romney for our party's nomination.
We face huge challenges, and we need a leader who understands the economy, recognises more government regulation is not the answer, believes in entrepreneurial capitalism and works to ensure that all Americans have the opportunity to succeed."
Mr Bush had been courted as a possible presidential candidate himself, and his father, former President George H W Bush, has also effectively endorsed Mr Romney's candidacy.
In another boost, FreedomWorks, an organisation that supports the Tea Party movement, dropped its opposition to Mr Romney's candidacy.
"It is a statistical fact that the numbers favour Mitt Romney," Russ Walker, vice-president of FreedomWorks told the Washington Times.
"We are dedicated to defeating Obama and electing a conservative Senate that will help Romney repeal Obamacare [healthcare reform] and address the nation's economic and spending challenges."
Mr Romney has consistently had difficulty winning over the Republican base, who have questioned his conservative credentials.
His senior advisor Eric Fehrnstrom told CNN on Wednesday that Mr Santorum and Mr Gingrich should now step aside.
"Ultimately I'm confident they'll make a decision that's not only right for their party but right for them," he told CNN.
'Competing every state'
On Tuesday, Mr Romney secured 47% of the Illinois vote, with a comfortable lead of 12 points over Rick Santorum, his closest rival.
Ron Paul polled 9% in Illinois and Newt Gingrich was on 8%; neither candidate campaigned extensively in the state.
"I'm running for president because I have the experience and the vision to get us out of this mess," said Mr Romney, as his victory became evident.
However, addressing supporters on Tuesday evening, Mr Santorum said he had polled well in Illinois in areas "that conservatives and Republicans populate".
We're very happy about that and we're happy about the delegates we're going to get, too," he said.
A candidate needs to accumulate 1,144 delegates to the August convention in order to secure the nomination.
Currently, Mr Romney has won 563 delegates versus Mr Santorum's 263, according to an estimate by the Associated Press.
Analysts say the current figures make it an almost impossible task for Mr Santorum, who has spoken openly in recent weeks about winning enough delegates to stop Mr Romney taking the crown.
Such an outcome would lead to a competitive vote at the Tampa convention, in which Mr Santorum feels he could overcome Mr Romney.
Mr Santorum has vowed to continue, "competing in every state", citing tepid support for Mr Romney even in states the former Massachusetts governor has won.
US media analysis
Blogging at the Washington Post, The Fix's Chris Cillizza says Mr Bush's endorsement of the Romney campaign is one of the few that actually matters, and can send a wider signal to the rest of the party and country.
The Bush endorsement of Romney will have significant reverberations across the media, activist and, perhaps most importantly, donor worlds that will likely have a negative impact on Santorum's ability to move forward in a viable manner.
"The one complicating factor in puzzling out the importance of the Jeb endorsement is the back story of why he decided to do it. Bush and those closest to him are mum on it but one senior party operative told the Fix earlier today that 'he's lost any hope that we'll have anyone better'."
Maggie Haberman, writing for Politico, says winning in Illinois was a significant step for Mr Romney, enabling the former governor to look and sound more presidential.
"His win was not a knockout, and Santorum — as well as Newt Gingrich and Ron Paul — will keep going.
"Even so, this was an important pivot point for Romney, who seemed noticeably more at ease in an election night speech that made no mention of his rivals and that sounded much more like a general-election message than the ones he's delivered on past primary nights."
The New Yorker's John Cassidy wrote that Mr Romney appeared to have found his stride while delivering his victory speech on Tuesday night.
"What nearly four months of trench warfare has really left Romney with is frighteningly high negative ratings from the independent voters he will need to win the White House; a depleted campaign bank account (doubtless he can refill it); and a number of hostages to fortune that the Obama campaign will be eagerly waiting to exploit.
"But last night, perhaps for the first time, the argument that Romney will be a better candidate for what he's been through didn't sound completely outlandish."