Hawaiian music played during the service, reflecting Inouye's love for his home state. Inouye was Hawaii's first congressman. His casket was carried into the cathedral by eight military pallbearers. Obama appeared to wipe tears from his eyes as he sat in the front row next to Biden and Clinton.
One speaker after another described Inouye as a political giant with refreshing humility. Obama said that Inouye ultimately decided he had done OK in representing his state and his nation.
"Danny, you were more than OK," Obama said. "You were extraordinary."
As a legislator, Inouye made his mark on the Senate Appropriations Committee, steering federal money back home to help build the kinds of roads, schools and housing that Americans on the mainland took for granted.
On Thursday, colleagues and aides lined the Capitol rotunda five deep to say farewell.
The rare ceremony demonstrated the respect and good will he generated over the years. Only 31 have lain in the Capitol rotunda; the last was former President Gerald R. Ford nearly six years ago.
Inouye's body will be returned to Hawaii on Saturday.
AP White House Correspondent Ben Feller contributed to this report.