WASHINGTON -  US President Donald Trump Friday walked out of an executive order signing ceremony without placing his signature on the orders after being questioned over his former National Security Adviser Michael Flynn and Russia.

Exactly a week after his vow to “repeal and replace” Obamacare health insurance 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,” Trump said, before handing over to Commerce Secretary Wilbur Ross and National Trade Council Director Peter Navarro.

At the ceremony, the question a reporter shouted was whether Flynn, who has offered to testify on the alleged Russian involvement in the US election in return for immunity from prosecution, would be granted immunity.

The president ignored the questions and went to another room. Vice President Mike Pence followed him with the folders containing the two executive orders.

Before leaving the room, Trump said, “Thank you everybody, you're going to see some very, very strong results very, very quickly. Thank you very much.”

Trump had earlier tweeted that Flynn “should ask for immunity because the investigations were a ‘witch hunt.’

"Mike Flynn should ask for immunity in that this is a witch hunt (excuse for big election loss), by media & Dems, of historic proportion!" Trump tweeted Friday.

Last week, Flynn agreed to testify as part of congressional probes into the matter as long as he is protected from prosecution.

Moments before he left the Oval Office, Trump had announced that the two orders would initiate a "great revival" for US manufacturing. He implied his campaign message in his speech again saying that trade pacts have caused factory jobs to flow overseas.

According to the White House, Trump later signed the orders aimed at identifying and targeting foreign trade abuses behind closed doors.

The completion of a large-scale report that will track trade deficits country-by-country and product-by-product is on the first order, while the other aims at improving the collection of duties on imports.