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."