US President-elect Donald Trump has observed a test launch of a giant spaceship being developed by Elon Musk's SpaceX, in what US media describe as a sign of growing closeness between the two men.

On Tuesday, SpaceX launched its Starship rocket from a facility in the southern US state of Texas with Trump and Musk in attendance.

Musk rallied support for Trump's reelection campaign. Trump announced last week that he would appoint Musk as co-leader of a new organization tasked with reviewing and considering reductions to government spending.

After the election, Musk has reportedly been spending a lot of time at Trump's Mar-a-Lago residence in the southern state of Florida. The entrepreneur is also said to have been present during phone calls between Trump and foreign leaders as well as during interviews with candidates for key positions in the incoming administration.

Major US media outlets have reported that Trump's appearance at Tuesday's event is a sign of their growing closeness and Musk's rising influence on Trump's decision making.