Obama first said in 2010 he wanted to send astronauts "to orbit Mars and return them safely to Earth" by the mid-2030s with "a landing on Mars" to follow.
In an opinion article Tuesday on CNN.com, Obama said the ultimate ambition was not only to send humans to Mars and bring them back, but to "remain there for an extended time."
"Getting to Mars will require continued cooperation between government and private innovators, and we're already well on our way," he said.
Obama’s article comes two weeks after
In a speech at the International Astronautical Congress in Mexico, Musk similarly called for a public/private partnership.
This week, Obama will speak at the White House Frontiers conference in Pittsburgh, an event that will focus on innovations in science and technology, including a future Mars mission. Executives from companies such as SpaceX, Virgin Galactic and moon mining firm Moon Express are also set to speak at the conference.
"It just underlines the theme that's run through the Obama administration, which is encouraging partnerships with the private sector, providing additional opportunities for work and, when appropriate, doing business in a slightly different way," said John Logsdon, professor emeritus of the Space Policy Institute at George Washington University.
"It's mainly about leaving a legacy," he said.
Analysts said a public/private partnership recognizes the reality of the space business today, as well as financial limitations.
"On the commercial side, there are a lot of innovative ideas," said Bill Ostrove, aerospace and defense analyst at Forecast International. "But they need that backing from the government both in the know-how … (and) the government's financial resources."
Smaller space start-ups that don't usually work with the government could benefit most from Obama's goal, said Eric Stallmer, president of the Commercial Spaceflight Federation trade group.
"I think it gives a level of excitement to a variety of different players," he said. "You don't know who the next SpaceX could be, or the next Blue Origin," referring to the space tourism company started by Amazon.com founder Jeff Bezos.
SpaceX, whose full name is Space Exploration Technologies Corp., has said its first test flight of an interplanetary vehicle could come in four years. A crewed mission could launch in late 2024 and arrive on Mars in 2025.
Developing the interplanetary transport system could cost SpaceX $10 billion.
In an email, SpaceX spokesman Phil Larson said it was "exciting to see President Obama advocate for the next frontier in human space flight," and that the company was looking forward to "participating in the journey."
The company's plan to send an unmanned Dragon spacecraft to the red planet as early as 2018 will provide an early chance to demonstrate how private space companies and NASA can work together, said Charles Lurio, publisher of the Lurio Report newsletter on entrepreneurial spaceflight.
SpaceX will use the flight to test landing capabilities, interplanetary navigation and other systems. NASA will provide some technical support for the mission because it is interested in the entry, descent and landing data.
Marco Caceres, senior space analyst at the Teal Group, estimated that a mission to Mars done the "traditional way" by NASA could cost at least $1 trillion. Oftentimes, large space programs can get delayed if Congress does not grant the requested funding amount, or if there are technical problems along the way.
A public/private partnership may speed up the timeline and could lower that cost below $1 trillion, Caceres said.
But one of the biggest questions is whether such a program could get funding from Congress, said Ostrove of Forecast International.
"There is some desire to do the actual exploration," he said. "I think that there's maybe not necessarily the political will to spend the money on these types of programs when there's so many other things we're facing now."
One question still to be answered is who will build the massive rockets needed to get to Mars.
NASA plans to send its Space Launch System rocket to an asteroid in the mid-2020s and to Mars in the 2030s. Boeing Chief Executive Dennis Muilenburg has said he thinks the first person to land on Mars will "arrive there riding a Boeing rocket," a reference to the company's role on the SLS project.
That is a challenge to Musk, who described a rocket booster measuring 39 feet in diameter. When stacked with the SpaceX Mars spaceship, the interplanetary transport system would be 400 feet tall.
In a statement Tuesday, John Elbon, vice president and general manager of Boeing Space Exploration, said that sending humans to Mars is "an achievable and inspiration goal for this country."
"This isn't science fiction," he said. "We're building real hardware right now and NASA has a solid plan to get there."
Meanwhile, new research pointed out the risks of any Mars flights. Scientists studying the potential effects of cosmic rays on astronauts' brains during deep space missions to Mars or beyond found that rodents who were exposed to radiation still suffered from brain inflammation and neural damage six months later.
Achieving Obama's Mars ambition, of course, will be out of his hands. SpaceNews reported last month that Democratic presidential nominee Hillary Clinton said she supported plans to send humans to Mars in response to a questionnaire on science policy from ScienceDebate.org.
Republican presidential nominee Donald Trump praised space exploration but did not say he supported a human Mars mission.
"Hopefully it's a challenge to the next administration," said Stallmer of the Commercial Spaceflight Federation.
Masunaga reported from Los Angeles and Puzzanghera from Washington.
4:55 p.m.: This article was updated with comments from analysts.
10:50 a.m.: This article was updated with comments from the Commercial Spaceflight Federation trade group.