"Do it," Musk tweeted Thursday in response to a story about the assertion.
Muilenburg was asked by The Street, "Who arrives to Mars first, SpaceX or Boeing?"
"Boeing," Muilenburg responded. A video of the interview was posted on The Street Thursday.
"We are working jointly with NASA and our industry team right now. We are building that first rocket space launch system. It's about 38 stories tall, the first article is being built right now. About 9.2 million pounds of thrust on that rocket, the biggest rocket ever," says Muilenburg.
"If you want to put that in car terms, that's about the equivalent thrust of 207,000 Corvettes and we are going to begin test flights starting next year."
Musk has also said SpaceX will start test flights for its rocket going to Mars in 2019.
In a question and answer session at South by Southwest in Austin March, Musk said, "we are building the first Mars, or interplanetary ship, and I think we'll be able to do short trips, flights by first half of next year."
Admittedly, Musk did acknowledge he sets overly aggressive deadlines. "Although sometimes, my timelines are a little, you know..." he said in Austin.
At the 2017 International Astronautical Congress in Adelaide, Australia, in September, Musk said he wants to land at least two cargo ships on Mars by 2022 and by 2024, he wants to bring send the land the first passengers on Mars.
Boeing and SpaceX are both partners and competitors, says Muilenburg.
"Well, it's a rivalry. It's competitive. In some places we work together. We launch satellites today on SpaceX rockets, but we also compete," the Boeing CEO says on The Street.
"It marks an important step in returning American astronauts to the moon for the first time since 1972 for long-term exploration and use," Trump said during the signing of directive. "This time we will not only plant our flag and leave our footprint. We will establish a foundation for an eventual mission to Mars and, perhaps, someday, to many worlds beyond."
Muilenburg said Boeing would start with the moon.
"We are going to go back to the moon. The Administration is really leaning forward on returning to the moon, setting up a lunar station and then using that as a stepping stone to Mars and I firmly believe that the first person that steps foot on Mars will get there on a Boeing rocket," Muilenburg told The Street.
While the competition between Boeing and SpaceX is palpable, Muilenburg says it's productive.
"I, frankly, think it is great to see so much interest in the space industry. Really, a rebirth of that. I see more energy in the space industry today than we have in decades. I think it is great for the country. And this competitive nature of the business is just making us all better and it makes Boeing better. And it makes us drive forward even faster," he says. "So, I am excited about the future of the space business."
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