"We cannot win this election," the Massachusetts senator said in an emotional campaign farewell in Boston.
In an appearance in Faneuil Hall where he launched his quest for the White House more than a year ago, Mr Kerry said of his call to Mr Bush: "We talked about the danger of division in our country and the need the desperate need for unity, for finding common ground and coming together.
"Today, I hope we can begin the healing."
Mr Kerry's twin concessions, one private, the other played out before supporters and a nationwide television audience, followed his decision not to contest Mr Bush's lead in make-or-break Ohio.
Ohio's 20 electoral votes gave Mr Bush 274 in the
Associated Press count, four more than the 270 needed for victory.
Mr Kerry had 252 electoral votes, with Iowa (7) and New Mexico (5) unsettled. Mr Bush was winning 51% of the popular vote to 48% for his rival.
He led by more than three million ballots.
Officials in both camps described the telephone conversation between two campaign warriors.
A Democratic source said Mr Bush called Mr Kerry a worthy, tough and honourable opponent.
Mr Kerry told the president the country was too divided, the source said, and Mr Bush agreed.
"We really have to do something about it," Mr Kerry said, according to the official.
White House spokesman Scott McClellan said Mr Bush told Mr Kerry: "I think you were an admirable, honourable opponent."
Mr Kerry placed his call after weighing unattractive options overnight.
With Mr Bush holding fast to a six-figure lead in Ohio, Mr Kerry could give up or trigger a struggle that would have stirred memories of the bitter recount in Florida that propelled Mr Bush to the White House in 2000.
The call was the last bit of drama in a campaign full of it.
He acted, hours after White House chief of staff Andy Card declared Mr Bush the winner and White House aides said the president was giving Mr Kerry time to consider his next step.
One senior Democrat familiar with the discussions in Boston said Mr Kerry's running mate, North Carolina Senator John Edwards, was suggesting he should not concede.
The official said Mr Edwards, a trial lawyer, wanted to make sure all options were explored and that Democrats pursued them as thoroughly as Republicans would if the positions were reversed.
Advisers said the campaign just wanted one last look for uncounted ballots that might close the 136,000-vote advantage Mr Bush held in Ohio.
An Associated Press survey of the state's 88 counties found there were about 150,000 uncounted provisional ballots and an unspecified number of absentee votes still to be counted.
Ohio aside, New Mexico and Iowa remained too close to call in a race for the White House, framed by a worldwide war against terror and economic worries at home.
But those two states were for the record Ohio alone had the electoral votes to swing the election to the man in the White House or his Democratic challenger.
Mr Bush remained at the White House, a GOP legal and political team dispatched overnight to Ohio in case Mr Kerry made a fight of it.
Republicans already were celebrating election gains in Congress.
They picked up at least three seats in the Senate, and a fourth was within their grasp, in Alaska. And they drove Democratic Senate Minority leader Tom Daschle from office.
That will be the state of play on Capitol Hill for the next two years, with the chance of a Supreme Court nomination fight looming along with legislative battles.
Republicans also reinforced their majority in the House.
Glitches galore cropped up in overwhelmed polling places as Americans voted in high numbers, fired up by unprecedented registration drives, the excruciatingly close contest and the sense these were unusually consequential times.
The country exposed its rifts on matters of great importance in yesterday's voting.
Exit polls found the electorate split down the middle, or very close to it, on whether the nation is moving in the right direction, on what to do in Iraq, on whom they trust with their security.
Bush built a solid foundation by hanging on to almost all the battleground states he got last time.
Facing the cruel arithmetic of attrition, Mr Kerry needed to do more than go one state better than Al Gore four years ago.
Redistricting since then had left those 2000 Democratic prizes 10 electoral votes short of the total needed to win the presidency.
Florida fell to Mr Bush again, close but no argument about it.
Mr Bush's relentless effort to wrest Pennsylvania from the Democratic column fell short. He had visited the state 44 times. Mr Kerry picked up New Hampshire in perhaps the election's only turnover.
In Ohio, Mr Kerry won among young adults, but lost in every other age group.
A quarter of Ohio voters identified themselves as born-again Christians and they backed Mr Bush by a three-to-one margin.
A sideline issue in the national presidential
campaign, gay civil unions may have been a sleeper that hurt Mr Kerry who strongly supports that right in Ohio and elsewhere.
Ohioans expanded their law banning gay marriage, already considered the toughest in the country, with an even broader constitutional amendment against civil unions.