SpaceX’s prototype is an early version of the spacecraft Mr Musk wants to send humans on to colonise Mars. It is set to make a 150m “hop” at the test site in Boca Chica, Texas, on Tuesday.
A last minute technical problem on Monday forced the test to be postponed.
Mr Musk greeted two Nasa astronauts, Doug Hurley and Bob Benken, on his company’s Crew Dragon capsule.
The SpaceX boss tweeted: “We’re going to go to the moon, we’re going to have a base on the moon, we’re going to send people to Mars and make life multi-planetary.”
He also tweeted: “When space travel becomes as common as air travel, the future of civilisation will be assured.”
Starship’s technology has been designed to have multiple uses in space.
It is intended to launch satellites into earth orbit, land crew on the moon for Nasa and, transport humans to another planet for the first time.
The final version of the Starship will be approximately 50m tall.
It will also have Raptor engines and launch on top of a SpaceX Super Heavy rocket power by 31 other raptors.
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SpaceX can now focus more on Starship after the astronauts Doug Hurley and Bob Behnken safely returned from a two-month test mission to the International Space Station on Crew Dragon.
The head of Nasa, Jim Bridenstine, said Mr Musk’s focus on Starship may have gotten in the way of the company meeting its commitments to Crew Dragon last year .
On Monday, Mr Bridenstine told Mr Musk: “I said that it’s time to deliver and you responded absolutely magnificently and you delivered.
“You delivered beyond what any of us would have expected.”
SpaceX, Nasa and the US Coast Guard conducted a review into how recreational boaters managed to come just a few feet of the mission’s capsule when it floated in the ocean awaiting recovery.
Mr Bridenstine said: “We need to do better.”
Colonel Hurley said inside the capsule, the crew were on SpaceX’s satellite telephone “bobbing around, making prank satellite calls to whoever we could get hold of.”
A recipient of a prank call was Anthony Vareha, a Nasa flight director on duty at Nasa’s Johnson Space Centre in Houston, Texas.
He said: “It started with an opening line like ‘Hi, it’s Doug and Bob and we’re in the ocean.
“I think my response was ‘Yeah, I can see that.’”