Donald Trump is facing calls to immediately seize control of SpaceX after Elon Musk threatened to abandon NASA astronauts in orbit amid a bitter fallout with the president.

In an explosive back-and-fourth on Thursday afternoon, Trump hit back to Musk's escalating claims by suggesting the entrepreneur's multibillion-dollar government contracts be taken away.

'The easiest way to save money in our Budget, Billions and Billions of Dollars, is to terminate Elon's Governmental Subsidies and Contracts,' Trump said on Truth Social.

Musk fired back, with the SpaceX chief saying he would begin 'decommissioning' his company's Dragon spacecraft in response.

The spacecraft is vital for ferrying NASA astronauts to and from the International Space Station.