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CHICAGO — A triumphant Barack Obama vowed to be a president for all America, even those who voted against him, and asked for patience to address the nation’s problems of war and finance that he called the greatest challenges of a lifetime.

The first black president-elect cast his election as a defining moment in the country’s 232-year history and a rebuke to cynicism, fear and doubt.

‘‘If there is anyone out there who still doubts that America is a place where all things are possible; who still wonders if the dream of our founders is alive in our time; who still questions the power of our democracy, tonight is your answer,’’ he said in his first public words after winning the election.

His victory speech was delivered before a multiracial crowd that city officials estimated at 240,000 people. Many cried and nodded their heads while he spoke, surrounded by clear bulletproof screens on his left and right.

He appeared on stage with his wife, Michelle, and daughters Malia, 10, and Sasha, 7, poised to become the first family of color ever to occupy the White House. Every family member dressed in black and red, and Obama told his daughters during his speech that they would get the puppy he promised would come with a victory.

‘‘Even as we celebrate tonight, we know the challenges that tomorrow will bring are the greatest of our lifetime — two wars, a planet in peril, the worst financial crisis in a century,’’ he said. ‘‘There is new energy to harness and new jobs to be created; new schools to build and threats to meet and, for us to lead, alliances to repair.’’

He was already suggesting a second term to accomplish his goals, saying he expected ‘‘setbacks and false starts.’’

‘‘We may not get there in one year or even one term,’’ he said. ‘‘But America, I have never been more hopeful than I am tonight that we will get there. I promise you — we as a people will get there.’’

To those who voted against him, he said, ‘‘I will be your president, too.’’

Obama, an Illinois senator born 47 years ago of a white American mother and a black African father, sprinkled his address with references to the civil rights struggle. He paid tribute to Ann Nixon Cooper, a 106-year-old daughter of slaves born at a time when women and blacks couldn’t vote. She cast her ballot in Atlanta Tuesday, Obama said.

He quoted another president from Illinois, Abraham Lincoln, and although he didn’t mention Martin Luther King Jr.’s name, he echoed King’s statement that ‘‘we shall overcome because the arc of the moral universe is long, but it bends toward justice.’’

Obama invited ‘‘those who have been told for so long by so many to be cynical, and fearful, and doubtful of what we can achieve to put their hands on the arc of history and bend it once more toward the hope of a better day.’’

The president-elect said he looks forward to working with Republican rival John McCain, who called him to concede as The Associated Press and television networks called the race at 11 p.m. EST. Obama spokesman Robert Gibbs said Obama thanked McCain for his graciousness and told him he had waged a tough race.

Gibbs quoted Obama as saying to McCain: ‘‘I need your help. You’re a leader on so many important issues’’

President Bush called Obama shortly after the Illinois senator hung up with McCain, and Vice President Dick Cheney called Obama running mate Joe Biden. Obama watched McCain’s concession speech from his suite in a downtown hotel, where he had watched returns with Biden, his extended family and senior campaign staff.

A few blocks away, the crowd in Grant Park that included celebrities Brad Pitt and Oprah Winfrey erupted into cheers to see their chosen candidate break the White House color barrier. Audience members leapt into the air, waving American flags.

The size of the group, spread out toward the Chicago skyline a few blocks in the distance, reflected the eye-popping crowds that Obama drew throughout his campaign. Even the weather favored Obama — the temperature was around 60 degrees as he spoke, unusual for a November night in Chicago.

Obama began the day by casting his vote with his wife and daughters at his side. He unwound while waiting for returns by playing two hours of basketball with friends and staff, then eating a steak dinner at home with his immediate family and in-laws.

He made a final Election Day campaign stop in Indiana, one of several longtime Republican strongholds in the presidential race that he tried to win. It was a symbolic ending of a campaign for a candidate who first made his name with an address to the Democratic National Convention four years ago in which he decried efforts to ‘‘slice and dice our country into red states and blue states.’’

He repeated that sentiment in his victory speech. ‘‘We have never been a collection of red states and blue states. We are, and always will be, the United States of America,’’ he said.