John McCain did a victory lap Wednesday, swinging by the White House for the endorsement of President Bush and meeting with the Republican National Committee leadership to talk strategy after clinching the GOP nomination the night before.

"I believe this election will be about very stark differences," he said during his visit to RNC headquarters, claiming he'd work closely with the party on fundraising and organization so that his campaign would be competitive in "literally every state."

Bush had formally welcomed McCain and his wife, Cindy, earlier at the North Portico of the White House. He hosted a lunch in his private dining room.

In offering his endorsement, Bush embraced his former rival from the 2000 presidential primary race and predicted McCain would be successful in defeating the Democratic nominee in November.

"John McCain is the nominee of the Republican Party," Bush said Wednesday. "John showed incredible courage, strength of character and perseverance in order to get to this moment, and that's exactly what we need in a president."

Bush highlighted national security concerns in his endorsement, saying "the country better have somebody in that Oval Office who understands the stakes, and John McCain understands those stakes."

Former President George H.W. Bush endorsed McCain two weeks ago.

McCain on Wednesday said he intends to hold campaign events with the president as much as his schedule will allow.

"I hope that the president will find time from his busy schedule to be out on the campaign trail with me, and I will be very privileged to have the opportunity of being again on the campaign trail with him," McCain said.

McCain swept the four states holding primary contests Tuesday night -- Vermont, Rhode Island, Texas and Ohio -- and earned enough delegates to put him over the 1,191-delegate threshold needed to seal the nomination. Seeing this, rival Mike Huckabee bowed out of the race Tuesday night.

With his low poll ratings and an unpopular war on his shoulders, though, Bush could hurt McCain with some groups, while helping him with others.

"If my showing up and endorsing him helps him -- or if I'm against him and it helps him -- either way, I want him to win," the president said. "This is an age-old question that every president has had to answer, and there is an appropriate amount of campaigning for me to do. But they're not going to be voting for me. ... I've had my time in the Oval Office."

"It's not about me," Bush said. "I've done my bit."

Earlier, McCain actually had kept Bush waiting for his visit.

Bush joked with reporters, laughing as he turned left and right in a jig as he waited for the Republican presidential nominee-in-waiting to arrive at the White House for the promised endorsement.

McCain finally showed up and the two men went inside for lunch. "He's going to win," Bush said. He shook hands with McCain and kissed his wife, Cindy, on the cheek.

In recent weeks, Bush has gone out of his way to defend the senator's conservative credentials, saying criticism of the Arizona senator has been grossly unfair. The two were bitter rivals in 2000.

"The president has said he looks forward to vigorously campaigning for the GOP and tonight it has become clear that the GOP nominee will be Sen. John McCain," White House press secretary Dana Perino said Tuesday night.

Bush made morning phone calls to McCain's former rivals Huckabee, Mitt Romney and Fred Thompson to congratulate them on their primary campaigns. He intends to call Rudy Giuliani later.

"He said he appreciated their ability to keep their sense of humor and that he looks forward to working [with] them in the '08 election," Perino said.

Asked about McCain's past disagreements with Bush, she said: "The point of these elections is for the candidate to run as their own person. Elections are about change and going forward, and one of the most attractive things about Sen. McCain to the Republican Party is that he has been his own person. He has blazed his own trail and he will have to make the case as to why voters should vote for him."

The Associated Press contributed to this report.