Donald Trump has stormed out of an executive order signing ceremony without signing the orders after being questioned over Michael Flynn and Russia.

Exactly a week after his vow to “repeal and replace” Obamacare imploded in Congress, the President told assembled reporters he was going to “get down to some serious business”.

The two executive orders, sitting on his desk in the Oval Office, aimed to put his drive for American trade and manufacturing jobs back at the top of the agenda, ordering a study into the cause of US trade deficits and a crackdown on import duty evasion.

“We're going to investigate all trade abuses, and, based on those findings, we will take necessary and lawful action to end those many abuses,” Mr Trump said, before handing over to Commerce Secretary Wilbur Ross and National Trade Council Director Peter Navarro.

But after Mike Pence hailed a “great day for the American economy” in a planned speech, Mr Trump took back the podium to cut the event short.

“Thank you everybody, you’re going to see some very, very strong results very, very quickly – thank you very much,” he said, before swiftly walking towards the door.

Mr Pence gave him a passing tap on the arm as other attendees at the signing ceremony appeared confused, with Mr Trump flashing a thumbs up before leaving the Oval Office.

Donald Trump leaves without signing executive orders on trade during a ceremony at the Oval Office of the White House on 31 March (AP)

The President appeared to become flustered as a reporter called out questions on his former national security adviser Mr Flynn, who Mr Trump claimed should “ask for immunity” in investigations into links between his administration and the Russian government.

“With your tweet, were you trying tell the Justice Department to grant immunity to Michael Flynn?” he could be heard asking.

“Were you trying to do that Mr President, was that your intention sir?”

The Vice President rushed to the doorway and had a brief word with his superior, presumably to tell him he had forgotten to sign the executive orders waiting on his desk.

Mr Trump motioned towards himself before disappearing into a corridor, leaving Mr Pence to collect the documents and lead the group out in front of bemused members of the press.

He is thought to have signed the orders later behind closed doors, with the White House publishing the full text online.

Vice President Mike Pence was left to collect the executive orders Donald Trump had been due to sign on 31 March (Reuters)

The incident unfolded on the White House’s official live stream of the event but was cut from an edited video later posted on Mr Trump’s personal Twitter account.

A lawyer for Mr Flynn said he was in talks with congressional committees investigating Russia’s alleged interference in the US election to testify before them in exchange for immunity from prosecution.

He was forced to resign from his role as national security adviser after admitting he gave the Vice President “incomplete information” about discussions with the Russian ambassador over sanctions.

Mr Trump took to Twitter to urge Mr Flynn to “ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion!”

Critics swiftly pointed out that the President had himself attacked the practice after Democratic staff were given immunity in the Hillary Clinton email investigation.

“If you're not guilty of a crime, what do you need immunity for?” he asked a supporters’ rally.

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“Have you ever seen anything so corrupt in your life? Have you ever seen a greater embarrassment to our country?”

Mr Trump has been struggling to move attention away from the continuing scandal over Russia’s alleged interference in his favour but has suffered several embarrassing defeats on his attempted immigration bans and healthcare reforms.

His latest executive orders came before he meets with Chinese President Xi Jinping in Florida, a summit that promises to be fraught with trade tensions.

Mr Trump said he and Mr Xi were “going to get down to some serious business” and vowed that “the theft of American prosperity” by foreign countries would end.

One of the orders directed the Commerce Department and the US trade representative to conduct a 90-day review of the causes of massive trade deficits, with the second trade will non-payment and under-collection of anti-dumping and anti-subsidy duties on foreign goods.