In remarks at the National Cathedral -- where Vice President Joe Biden, Senate Majority Leader Harry Reid, D-Nev., Sen. John Kerry, D-Mass., Sen. Joe Lieberman, Ind-Conn., and former President Bill Clinton were also in attendance -- Obama said Inouye was his "earliest political inspiration" as a member of the Senate Watergate Committee.
Obama recalled watching the Watergate hearings with his mother as a child in Hawaii, which Inouye represented in the Senate for nearly 50 years before his death Monday at age 88.
The president recalled how, as the child of a white mother and black father, he had been fascinated by "this man of Japanese descent ... full of dignity and grace."
"We remember a man who inspired all of us with his courage and moved us with his compassion, that inspired us with his integrity, and who taught so many of us, including a young boy growing up in Hawaii, that America has a place for everyone," Obama said.
He said Inouye, who had experienced discrimination because of his Japanese heritage, did not project the conventional image of a U.S. senator, yet he "commanded the respect of an entire nation."
Obama said Inouye "embodied the very best of aloha."
Reid said Inouye "lived a full and productive life" and "died as he lived -- with great dignity."
"Daniel Inouye advocated for the rights of all Americans -- regardless of the color of their skin or where their parents were born or what their religion was," Reid said.
Inouye's casket was carried into the cathedral by an eight-member U.S. military honor guard. The body of the World War II veteran and Medal of Honor recipient had lain in state at the Capitol Rotunda.