"I would not give up this fight if there was a chance we could prevail," said Kerry, who called Bush earlier on Wednesday to end the suspense of a vote-counting battle in the decisive state of Ohio.
"There won't be enough outstanding votes for us to be able to win Ohio, and therefore we cannot win this election," Kerry told supporters in Boston's historic Faneuil Hall, telling them: "Don't lose faith."
Bush aides said the president told Kerry he was an "admirable, worthy" opponent during the phone call, which concluded their bitter and close eight-month struggle for the White House.
In a dispute that evoked memories of the prolonged election recount in Florida in 2000, questions about provisional and absentee ballots in Ohio had delayed the final outcome of the presidential election for hours.
Bush congratulated Kerry on a
Ohio's 20 electoral votes were the final hurdle to Bush capturing an Electoral College majority of 270 votes after a divisive campaign that focused on the war in Iraq, the battle against global terrorism and the economy.
Republicans also celebrated expanded majorities in the House of Representatives and the Senate in results likely to build the president's mandate and ease Bush's conservative agenda in Congress.
Bush captured a majority of the popular vote, unlike the disputed 2000 election against Democrat Al Gore. With 99% of precincts reporting, Bush had 51% of votes against Kerry's 48%.
Kerry called Bush after meeting running mate John Edwards and Senator Edward Kennedy, his colleague from Massachusetts in the US Senate. Bush told Kerry he should be proud of the presidential campaign he ran, the White House
"You waged one tough campaign. I hope you are proud of the effort you put in. You should be," Bush told Kerry, according to White House spokesman Scott McClellan.
Kerry said he congratulated Bush and they discussed the country's divisions and "the desperate need for unity, for finding the common ground, coming together. Today I hope that we can begin the healing".
"You waged one tough campaign. I hope you are proud of the effort you put in. You should be"
US President George Bush
Ohio's Republican secretary of state Ken Blackwell had estimated as many as 175,000 provisional ballots could be cast, and counties reported as of Wednesday morning that 135,149 had been issued.
Republicans will hold at least 54 of the 100 Senate seats, three more than they now have, and widen their slim majority of the 435-member House in the new 109th Congress, set to convene on 3 January.
With 270 electoral votes needed to win the White House, Bush had captured 29 states with 274 electoral votes. Kerry won 19 states and the District of Columbia and 252 votes. Bush held a lead of 3.5 million votes over Kerry nationwide with 99% of the precincts reporting.
Still undecided were Iowa and New Mexico, but only Ohio could make either candidate a winner.