"I look forward to a good, spirited contest," the president said.
Bush spoke with reporters in the Oval Office during a photo opportunity with the prime minister of Iceland, David Oddsson.
Bush said Vice President Dick Cheney had called Edwards after the announcement was made to say he welcomed him to the race, "as do I."
Cheney placed the call just after 10 a.m. EDT to congratulate him, said Cheney's spokesman, Kevin Kellems.
"He thought it was the appropriate thing to do, and recalled the president having phoned Senator Kerry at a similar juncture, when it was clear he would be the nominee," Kellems said. He described the conversation as "brief and cordial."
"The vice president said that he looked forward to their debate, and a spirited campaign that he hopes will reflect credit on the process," Kellems said.
Cheney and Edwards are scheduled to debate Oct. 5.
The North Carolina Republican Party is critical of the liberal Democratic ticket.
In a statement, GOP Chairman Ferrell Blount says, "While Democrats would like to think that Edwards can help John Kerry by wooing Southern voters with his smooth Southern drawl, the reality is that neither Edwards nor Kerry are in tune with Southern voters; the only difference between the two senators is their accents."
State GOP officials say Kerry and Edwards are out of touch with the needs of North Carolina voters.
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