Elon Musk made his debut public appearance with Donald Trump at the White House Tuesday to announce fresh powers to overhaul the US government — even if the tech tycoon's son tried to steal the show.

Dressed in a black "Make America Great Again" cap, black t-shirt and overcoat, the SpaceX and Tesla tycoon spoke to reporters in the Oval Office while the US president sat behind the historic Resolute Desk.

Tasked by Trump to lead federal cost-cutting efforts through his "DOGE" agency — the so-called Department of Government Efficiency — Musk warned that the United States would go "bankrupt" without cuts.

The world's richest man rejected criticisms of a lack of transparency and possible conflicts of interest. He admitted he would make "mistakes" but said he would be tackling what he called the power of an "unelected" bureaucracy.

Trump signed an order that was set to give DOGE extra powers to order the heads of government departments to prepare for more of the cuts that have shaken the United States.

Critics have blasted the Musk-led cuts as unconstitutional concentration of power in the presidency.

But for a few seconds at least, Musk had something else to worry about.

'Gravitas can be difficult'

"Gravitas can be difficult sometimes," said Musk as his young son X — full name X Æ A-Xii — began to chatter and squirm during his remarks. 

At other times the boy, dressed in a tan overcoat, knelt down and leaned against Trump's desk as Musk's comments drew near the half-hour mark. 

As Musk talked about consumer debt at one point, the boy picked his nose.

It was a typically unorthodox appearance by Musk, whose iconoclastic style was a large part of the attraction for Trump as he sought a front-man for his sweeping overhaul of the US government.

Musk, who was the biggest donor to Trump's election campaign to the tune of a quarter of a billion dollars, has brought in a team of young engineers to drive a ruthless efficiency program.

The plans have effectively shuttered some federal agencies and sent staff home — and have sparked legal battles across the country and sparked accusations of an illegal power grab.

Asked by a reporter about his "detractors," Musk first joked "I have detractors? I don't believe it" — before claiming that thanks to Trump's election win "you couldnt ask for a stronger mandate from the public." 

"The people voted for major government reform and that's what people are going to get," said Musk. 

'Unelected'

Musk has also drawn accusations of hypocrisy given that he regularly rails against "unelected" bureaucrats — while he himself is an unelected official wielding huge power, yet answering media questions for just the first time since Trump returned to office.

The tech baron has also faced questions about potential conflicts of interest given that SpaceX has billions of dollars in contracts with the same government that he is auditing. 

Musk rejected the criticisms, saying he was being "transparent" and adding: "It's not like I think I can get away with something, I'll be scrutinized non-stop."

As he spoke about transparency, the Associated Press said that its White House reporter was barred from the Musk event over the top US news agency's refusal to follow Trump's order renaming the Gulf of Mexico as the Gulf of America.

After Musk, it was Trump's turn to speak, as he hailed Musk's work so far and embarked on a lengthy rant against US judges who are blocking some of their plans.

That left the elephant in the room. Or rather — how can one room as cramped as the Oval Office accommodate two powerful egos who are used to getting their own way?

Time Magazine's latest issue caused a stir with a cover featuring Musk behind the same Resolute Desk.

Musk however moved to show that he knew who is the boss. "I check frequently with the president to make sure that this is what the president wants to happen. So, we talk almost every day," he said.