The men accepted the awards from the former president's daughter, Caroline, at a ceremony at the John F. Kennedy Library attended by several members of Congress and the Kennedy family.
Murtha, a decorated combat veteran and conservative Democrat with a long history of supporting the military, broke ranks with the Bush administration in November, when he called for withdrawal of troops from Iraq.
"Today my words of Nov. 17, 2005, and the many that followed, reflect not only my gut consciousness but that of many in our military and the majority of this country," Murtha said. "I am proud to be the messenger of those who at one time had no voice."
Murtha's change of heart helped shape the public debate over the war, because of his reputation as a Democratic hawk and retired Marines Reserves colonel who enjoyed easy access to presidents.
The award committee said Murtha's decision "made him the target of withering political attacks and resulted in efforts by political opponents to discredit his Vietnam War decorations."
Appearing Monday on CBS' The Early Show, Murtha said, "All the things they said were illusion. They said how much better it was getting and every progress I saw was mischaracterized, misrepresented. So I felt an obligation to speak out in order to try to turn this thing around."
Mora, formerly one of the Pentagon's top civilian lawyers, fought a 2½-year behind-the-scenes battle with Pentagon brass and civilian leaders over U.S. military policies regarding detainees — policies he said could invite abuse.
"We need to be clear. Cruelty disfigures our national character," Mora said. "It is incompatible with our constitutional order, with our laws, and with our most prized values. Cruelty can be as effective as torture in destroying human dignity, and there is no moral distinction between one and the other."
Mora retired this year and now is a general counsel for Wal-Mart.
Asked if he had to struggle with his decision, Mora told Early Show Co-Anchor Julie Chen, "There was no struggle at all. It was very easy. In fact, there was never any other option. The fact that a policy of cruelty is against our values and laws was clear to me from the start."
Among those in attendance were Sen. Edward M. Kennedy, House Minority Leader Nancy Pelosi, a California Democrat; Massachusetts Congressmen Barney Frank and Stephen Lynch and various Kennedy family members.
"My father recognized that courage is really essential for leadership," Caroline Kennedy said Monday, also on CBS, "and so one of the ways that we honor his memory is by celebrating political courage today.
The John F. Kennedy Profile in Courage Award, created in 1989, is named for President Kennedy's Pulitzer Prize-winning book, "Profiles in Courage," which recounts the stories of eight U.S. senators who risked their careers to fight for what they believed in.
Past recipients of the award include former U.S. President Gerald Ford, Ukraine President Viktor Yushchenko, and U.S. Sens. John McCain and Russell Feingold.