"With courage unmeasured and unbounded love for his country, he walked where man had never walked before. The moon will miss its first son of earth," Romney said.
NASA Administrator Charles Bolden recalled Armstrong's grace and humility.
"As long as there are history books, Neil Armstrong will be included in them, remembered for taking humankind's first small step on a world beyond our own," Bolden said in a statement.
Armstrong's modesty and self-effacing manner never faded.
When he appeared in Dayton in 2003 to help celebrate the 100th anniversary of powered flight, he bounded onto a stage before 10,000 people packed into a baseball stadium. But he spoke for only a few seconds, did not mention the moon, and quickly ducked out of the spotlight.
He later joined Glenn, by then a senator, to lay wreaths on the graves of Wilbur and Orville Wright. Glenn introduced Armstrong and noted it was 34 years to the day that Armstrong had walked on the moon.
"Thank you, John. Thirty-four years?" Armstrong quipped, as if he hadn't given it a thought.
At another joint appearance, the two embraced and Glenn commented: "To this day, he's the one person on earth I'm truly, truly envious of."
Armstrong's moonwalk capped a series of accomplishments that included piloting the X-15 rocket plane and making the first space docking during the Gemini 8 mission, which included a successful emergency splashdown.
In the years afterward, Armstrong retreated to the quiet of the classroom and his southwestern Ohio farm. Aldrin said in his book "Men from Earth" that Armstrong was one of the quietest, most private men he had ever met.
In the Australian interview, Armstrong acknowledged that "now and then I miss the excitement about being in the cockpit of an airplane and doing new things."
At the time of the flight's 40th anniversary, Armstrong again was low-key, telling a gathering that the space race was "the ultimate peaceful competition: USA versus U.S.S.R. It did allow both sides to take the high road with the objectives of science and learning and exploration."
Glenn, who went through jungle training in Panama with Armstrong as part of the astronaut program, described him as "exceptionally brilliant" with technical matters but "rather retiring, doesn't like to be thrust into the limelight much."
Derek Elliott, curator of the Smithsonian Institution's U.S. Air and Space Museum from 1982 to 1992, said the moonwalk probably marked the high point of space exploration.
The manned lunar landing was a boon to the prestige of the United States, which had been locked in a space race with the former Soviet Union, and re-established U.S. pre-eminence in science and technology, Elliott said.
"The fact that we were able to see it and be a part of it means that we are in our own way witnesses to history," he said.
The 1969 landing met an audacious deadline that President John F. Kennedy had set in May 1961, shortly after Alan Shepard became the first American in space with a 15-minute suborbital flight. (Soviet cosmonaut Yuri A. Gagarin had orbited the Earth and beaten the U.S. into space the previous month.)
"I believe this nation should commit itself to achieving the goal, before the decade is out, of landing a man on the moon and returning him safely to Earth," Kennedy had said. "No single space project in this period will be more impressive to mankind, or more important to the long-range exploration of space; and none will be so difficult or expensive to accomplish."
The end-of-decade goal was met with more than five months to spare. "Houston: Tranquility Base here," Armstrong radioed after the spacecraft settled onto the moon. "The Eagle has landed."
"Roger, Tranquility," Apollo astronaut Charles Duke radioed back from Mission Control. "We copy you on the ground. You've got a bunch of guys about to turn blue. We're breathing again. Thanks a lot."