US President George W Bush has endorsed John McCain's White House bid after the Vietnam veteran sealed the Republican nomination on Tuesday.
Mr Bush said his one-time rival would be a president with the "determination to defeat an enemy and a heart big enough to love those who hurt".
Tuesday's voting also delivered three victories for Hillary Clinton, reviving her flagging Democratic campaign.
She hailed her wins as proof she was the party's strongest candidate.
DEMOCRATIC DELEGATE RACE
BARACK OBAMA: 1,567
Delegates won on 4 March: 173
States won: 24
HILLARY CLINTON: 1,462
Delegates won on 4 March: 185
States won: 16
Delegates needed to secure nomination: 2,025. Source: AP at 0530 GMT
But her rival Barack Obama, who won in Vermont, said he had an "insurmountable lead" and was "very confident".
Mrs Clinton still trails Mr Obama in the battle for the delegates who will seal the nomination at the Democratic party convention in August.
But her wins - 54% of the vote to Mr Obama's 44% in Ohio, and by 51% to 47% in Texas, as well as victory in the smaller prize of Rhode Island - are being seen as a huge psychological boost for her campaign.
President Bush said Mr McCain was "going to win" as the presumed nominee and his wife arrived at the White House.
Addressing reporters in the Rose Garden, Mr Bush described the man he defeated in the 2000 Republican primaries as a friend.
"I've got to know him well, I've campaigned against him and with him," he said.
Mr McCain said he had "great admiration, respect and affection" for the US president.
When asked whether too much support from Mr Bush, with his current low approval ratings, could damage his campaign, Mr McCain said: "I hope he'll campaign for me as much as is in keeping with his busy schedule."
He also reaffirmed a pledge made in his victory speech to fight a "respectful" campaign.
Mr McCain, who had been comfortably ahead, clinched the Republican nomination on Tuesday following a remarkable comeback after his campaign was all but written off following setbacks last summer.
In the Democratic race, the two contenders launched into a fresh round of campaign rhetoric.
"I think last night I proved that I'm the person most likely to win for the Democrats," Mrs Clinton said on Fox News.
Asked on CBS's Early Show about the possibility of a joint ticket with Mr Obama, she said: "Well, that may, you know, be where this is headed.
"But of course, we have to decide who's on the top of the ticket, and I think that the people of Ohio very clearly said that it should be me."
Mr Obama, who had won 11 contests in succession in the month before the 4 March polls, said it was "very premature to start talking about a joint ticket".
He pointed out that Mrs Clinton had "barely dented" the delegate count, despite her wins.
In total, according to the Associated Press, Mrs Clinton still trails Mr Obama with 1,462 delegates to his 1,567.
But the results from the Texas caucuses - meetings at which voters gather to indicate their support for their chosen candidate - have not been finalised, so with 12 delegates still to be awarded, the final count is not yet known.
Mr Obama, however, also reflected on his losses in later comments, saying Mrs Clinton "went very negative over the last week" and her campaign's strategy had "had some impact".
In response to her campaign's suggestions that she is better equipped to handle a foreign policy crisis than him, he targeted her credentials:
"What exactly is this foreign policy experience?" Mr Obama asked. "Was she negotiating treaties? Was she handling crises? The answer is no."
"We're happy to join the debate, if that's the debate they want to have," he said, as an aide promised "the vetting of Hillary Clinton" had "yet to start".
BBC diplomatic correspondent Jonathan Marcus says the next major battle is the Pennsylvania primary on 22 April.
If Mr Obama wins, Mrs Clinton may well be finished, he says, but if she wins, the race will go to the wire.
Correspondents say the race could continue right up until the party convention and be decided by the votes of senior party officials known as "super-delegates", who can choose for themselves which candidate to back.