WASHINGTON — President Bush won four more years in the White House on Wednesday and pledged to "fight this war on terror with every resource of our national power." John Kerry conceded defeat rather than back an election challenge in make-or-break Ohio.

"I will need your support and I will work to earn it," the president said in an appeal to the 55 million Americans who voted for his Democratic rival. "We are entering a season of hope," he said.

The president spoke before thousands of cheering supporters less than an hour after his vanquished rival conceded defeat. "We cannot win this election," the Massachusetts senator said in an emotional campaign farewell in Boston.

The re-election triumph gave the president a new term to pursue the war in Iraq and a conservative, tax-cutting agenda at home — and probably the chance to name one or more justices to an aging Supreme Court.

He also will preside alongside expanded Republican majorities in Congress. The GOP gained four Senate seats and bolstered its majority in the House by at least two.

Vice President Dick Cheney told the Republican victory rally that the results of Tuesday's elections translated into a mandate for the president's policies. He did not elaborate.

Bush sketched only the barest outline of a second term agenda, talking of reforming an "outdated tax code," overhauling Social Security and upholding the "deepest values of family and faith."

The two public appearances signaled the end of a campaign waged over the anti-terror war and the economy.

Hours earlier, Kerry had telephoned Bush to offer a private concession. Aides to both men stressed they had agreed on a need to heal the nation after a long and frequently bitter campaign.

Ohio's 20 electoral votes gave Bush 274 in the Associated Press count, four more than the 270 needed for victory. Kerry had 252 electoral votes, with Iowa (7) and New Mexico (5) unsettled.

Bush was winning 51 percent of the popular vote to 48 percent for his rival. He led by more than 3 million ballots.

Officials in both camps described the telephone conversation between two campaign warriors.

A Democratic source said Bush called Kerry a worthy, tough and honorable opponent. Kerry told Bush the country was too divided, and Bush agreed, the source said.

Yet Kerry's public remarks contained an element of challenge to the Republican president. "America is in need of unity and longing for a larger measure of compassion," he said. "I hope President Bush will advance those values in the coming years."