In overtly political passages, Mr Obama sent a message to his beleaguered supporters not to give up and that King's struggle remained unfinished as election year approaches.
"Nearly 50 years after the march on Washington, our work, Dr King's work, is not complete," he told a crowd of thousands gathered not far from where the preacher from Georgia delivered his famous "I Have a Dream" speech in August 1963.
President Barack Obama speaks during the dedication of the Martin Luther
King Jr. Memorial
Reminding the crowd of thousands that King had before his assassination in 1968 fought for "economic justice" and marched with workers seeking fair pay, Mr Obama said that inspiration needed to be drawn from earlier struggles.
"When met with hardship, when confronting disappointment, Dr King refused to accept what he called the 'is-ness' of today. He kept pushing towards the 'ought-ness' of tomorrow," said Mr Obama.
"When thinking about the work we must do – rebuilding an economy that can compete on a global stage, fixing our schools so that every child gets a world-class education, making sure that our health care system is affordable and accessible to all – let us not be trapped by what is, we've got to keep pushing for what ought to be," he said.
Referring to protests against the wealthy and the corporate culture that have spread from New York around the country and overseas, Mr Obama said: "Dr. King would want us to challenge the excesses of Wall Street without demonising those who work there."
The 30ft high pink granite monument to King is the first dedicated to a black American, and the first to a non-president or non-war hero on the National Mall, the capital's hallowed central park.
Fifteen years in the making, its designers could not have predicted then that the monument would be dedicated by the nation's first black president, just as in the heady days after Mr Obama's election it could scarcely have been predicted that he would face such bleak re-election prospects now.
Using the occasion, which was delayed after a hurricane hit Washington in August, as something of a spring board for his re-election, Mr Obama invoked the slogan from his 2008 campaign, reminding Americans that "change has never been quick".
"Change has never been simple, or without controversy. Change depends on persistence, change requires determination," he said.
Mr Obama, who sets off today on a three-day "American Jobs" bus tour, went on to admonish the "powerful and the privileged" for dismissing calls for change as attempts to destabilise the country.
The monument attracted some controversy as it was made and designed in China, but any complaints are likely to be forgotten now that King has taken his place halfway between the Lincoln and Jefferson memorials, and near the Roosevelt Memorial on what Harry Johnson, president of the foundation that undertook the project, called "a visual line of leadership".
Called the "Stone of Hope", the statue in the likeness of King shows him gazing sternly out onto the horizon, arms folded.
John Lewis, a Georgia congressman and one of few surviving veterans of the civil rights protests, said: "It is unreal, it is unbelievable that we are going to unveil this unbelievable monument to a man who was never elected to public office.
"If it hadn't been for Martin Luther King we would be a divided nation. If it hadn't been for Dr King we would have something akin to another civil war. He freed not only a people but a nation."
In polls, most Americans say there has been progress toward King's dream, but that a gulf still exists between blacks and whites.
"We are not still fully integrated in this country, there is no question about that," said Hilary Shelton of the National Association for the Advancement of Coloured People.
"At the time Dr King became involved, states could treat African-Americans differently than white Americans and everyone else. Because of his hard work, dedication, and his ultimate sacrifice, that country moved in a much better direction. A lot has been done and so much work has still to be done."