Francis and Obama were to hold talks in the White House after the ceremony. Both men see eye-to-eye on issues such as climate change and defense of the poor but hold different views on abortion rights and gay marriage.
The pope paraphrased King's 1963 "I Have A Dream" speech, saying that the world has "defaulted on a promissory note" to the planet and millions of marginalized people.
"American Catholics are committed to building a society which is truly tolerant and inclusive, to safeguarding the rights of individuals and communities, and to rejecting every form of unjust discrimination," he said.
Francis gave his support to traditional marriage in his remarks, pointing out that he will travel to Philadelphia later in his six-day visit to the United States for a meeting of Catholics "to celebrate and support the institutions of marriage and the family."
After the White House meeting, thousands of spectators lined the periphery of the National Mall to catch a brief glimpse of Francis during the papal parade to his mass with U.S. bishops.
When he paused at points along the route to wave, roars of approval rose from the crowds.
"The Holy Father is the successor of St. Peter, who was very first pope," said Catholic Debbie Littleton, 60, who traveled from Maine to be in Washington for the visit. "When he comes in our age, we come to tell him we love him."
Al Jazeera and wire services. Naureen Khan ocntributed to this report.