He noted that the lunar landing had taken place 66 years after the Wright brothers' first powered flight and called for a target of a manned landing on Mars by 2035, 66 years after the Apollo 11 landing.
Aldrin, the second man to walk on the Moon, and Collins were making a rare joint appearance at Washington's National Air and Space Museum on Sunday alongside Neil Armstrong, the first man on the Moon.
Armstrong, who has become famous for saying little about the Moon landings since his return and shunning almost all media interviews, gave a short lecture which only briefly touched on the Moon landing itself.
Instead his speech looked at the inventions and discoveries that led to his historic "giant leap for mankind" on July 20, 1969.
The space race of the 1960s he said was "the ultimate peaceful competition: USA versus USSR. It did allow both sides to take the high road with the objectives of science and learning and exploration".
"Eventually it provided a mechanism for engendering co-operation between former adversaries and in that sense, among others, it was an exceptional, national investment for both sides."\
Critical of plans
Pushing the Mars theme, Collins - the third member of the Apollo 11 team who circled the Moon but did not land on it - appeared critical of current Nasa plans for a return to the Moon, which he said could bog down more ambitious exploration.
Mars, he said, held far more potential interest to humanity than the Moon.
"Sometimes I think I flew to the wrong place," he said.
"Mars was always my favourite as a kid and it still is today ... I'd like to see Mars become the focus, just as John F Kennedy focused on the Moon."
Speaking alongside the three astronauts, the man who founded and directed Nasa's mission control said setting the goal of a new destination would generate inspiration and new knowledge above and beyond that of Apollo and was worth investing in.
"What we need is new technology; we have not had that since Apollo," Christopher Kraft Jr said.
Addressing the US president he added: "I say to Mr Obama: Let's get on with it. Let's invest in the future."
Monday's anniversary of the Moon landing is set to be marked by a series of events, including a meeting for the three Apollo astronauts with Barack Obama, the US president.
They are expected to again raise the cause of a mission to Mars.
The idea of a manned Mars mission has become a pet project for Aldrin in particular, who has used his celebrity to push for increased funding and support for manned space flights.
Obama has said he is keen to see a renewed US leadership in space exploration, but at a time of economic difficulties Nasa, the US space agency, is facing growing questions over its budget.
The agency's only manned space craft, the shuttle, is due to be retired next year with most estimates putting its replacement, Project Orion, at least six years away from flying.
At the same time several other nations are stepping up their efforts in space exploration, with many experts saying the next man to set foot on the Moon could be Chinese.