Republicans said they opposed Mr. Liu's nomination because they worried the University of California at Berkeley law professor would be an liberal activist judge who would play fast and loose with the Constitution from the bench. They also cited statements he has made suggesting support of affirmative action and gay marriage as individual rights.
Mr. Liu's lack of judicial experience — he has never served as a trial lawyer or judge — also has been noted.
The president tapped Mr. Liu more than a year ago to fill a vacancy on the 9th U.S. Circuit Court of Appeals, which includes California and much of the rest of the West. His nomination stalled in the Senate last year amid Republican opposition, and Mr. Obama renominated him for the post in January.
A procedural vote on May 19 to break the GOP-lead filibuster and allow Mr. Liu's nomination to proceed toward a final straight up-or-down vote fell eight votes shy of the 60 needed.
Mr. Liu's supporters say he is among the brightest young legal minds in the country and that he has been unfairly demonized by the political right.
They added he has received endorsements from several prominent conservatives off Capitol Hill, including Kenneth W. Starr, the independent counsel during President Clinton's Whitewater and Monica Lewinsky scandals.
The Liu debate extended far beyond Capitol Hill, as liberal, conservative and ethnic-minority groups saw the nomination fight as a crucial test of the president's ability to leave his mark on the nation's judiciary.
"Last week's loss would not have occurred had Republicans considered Professor Liu's record as a whole rather than cherry-picking certain passages and quotes out of context," said Tina Matsuoka, executive director of the National Asian Pacific American Bar Association.
Mr. Liu, 40, was born in Augusta, Ga., of parents who immigrated from Taiwan.
He is the first of 25 judicial nominations sent to the full Senate this year who hasn't been confirmed.
"I am profoundly indebted to you for your confidence in me and to the many people who have worked tirelessly in support of my nomination," said Mr. Liu told the president in his letter.
The White House as of Wednesday evening had not publicly responded to Mr. Liu's request.