"I'm thinking about you," Bush was quoted as saying.
Ken Mehlman (search), campaign manager for the Bush-Cheney campaign, said the pair talked by telephone shortly before 8 p.m. EST. He quoted Bush as saying, "You had an important victory tonight."
Kerry won a string of Super Tuesday contests, forcing John Edwards (search), his sole major rival, from the race.
Mehlman said Bush told Kerry that he looked forward to a "spirited contest." According to the Republican campaign manager, Kerry told Bush he hoped to keep the campaign "on the issues."
Kerry said he and Bush had a "very nice conversation."
"He called to congratulate me. I said I hope we have a great debate about the issues before the country," Kerry told reporters at his election-night party in downtown Washington.
Kerry watched Edwards' speech live on TV, with his wife, Teresa Heinz Kerry, Sen. Edward Kennedy of Massachusetts and staff.
Kerry said he didn't know Edwards had decided to drop out of the race until he saw an Associated Press headline flash across the television screen.
"It says he quit," Kerry said. "I didn't think he'd say that."