Holbrooke, 69, the president's special envoy for Afghanistan and Pakistan, was described as being in critical condition after undergoing surgery on a torn aorta.
The veteran diplomat was meeting with Secretary of State Hillary Rodham Clinton at the State Department on Friday when he suddenly collapsed and was rushed to George Washington University Hospital a few blocks away.
His family as well as Clinton and Adm. Mike Mullen, chairman of the Joint Chiefs of Staff, have been with Holbrooke at the hospital.
"Richard Holbrooke is a towering figure in American foreign policy, a critical member of my Afghanistan and Pakistan team, and a tireless public servant who has won the admiration of the American people and people around the world," Obama said in a statement.
Obama said he had spoken to Holbrooke's wife, Kati, on Saturday "and told her that Michelle and I are praying for Richard."
"We continue to pray for his recovery, and support his family in this difficult time," said the president..
Hospital officials referred all questions about Holbrooke's to the State Department.
Earlier, State Department spokesman P.J. Crowley said the surgery on Holbrooke's torn aorta a large artery taking blood from the heart was completed Saturday morning.
Clinton visited the hospital on Friday night and again Saturday.
Obama early in his administration named Holbrooke special envoy for Afghanistan and Pakistan.
The veteran diplomat is perhaps best known for helping broker the 1995 agreement that ended the war in Bosnia.
He served as U.S. ambassador to the United Nations during the Clinton administration. He also was U.S. ambassador to Germany from 1993 to 1994 and then assistant secretary of state for European affairs.
Holbrooke's career with the foreign service dates back to his posting in South Vietnam in 1962 and included time as a member of the U.S. delegation to the Paris Peace Talks on Vietnam.