US President Donald Trump has faced pressure from Republican allies in Congress over domestic abuse allegations against a former aide.

Politicians have questioned whether the Trump administration has properly vetted top staffers.

Republican Representative Trey Gowdy, chairman of the House Oversight Committee, said he was investigating when the White House learned of "potential derogatory or disqualifying information" about former Staff Secretary Rob Porter.

Mr Porter left the White House last week after two former wives said he abused them.

"The chronology is not favorable for the White House," Mr Gowdy said on CNN.

Republican House Speaker Paul Ryan, meanwhile, said the White House should improve its vetting process.

"If a person committing domestic violence gets into government, then there's a breakdown in the system," Mr Ryan said at a news conference.

Mr Porter's departure has raised questions about how long top staffers like White House Chief of Staff John Kelly knew about the allegations and whether it was a security risk to have Mr Porter working in the White House.

Some officials within the White House and some of the president's outside advisers have singled out Mr Kelly for criticism for his handling of the episode.

One source said Mr Trump has talked privately about replacing Mr Kelly.

A variety of names has been making the rounds as potential replacements, such as top White House economic adviser Gary Cohn, the source said.

Vice President Mike Pence told the Axios media outlet that the White House could have handled the Porter case better but that he has great respect for Mr Kelly.

"John Kelly has done a remarkable job as chief of staff for the president of the United States, and I look forward to continuing to work with him for many, many months to come," Mr Pence said.

Mr Trump himself declined to answer shouted questions about Mr Kelly.

White House speechwriter David Sorensen resigned on Friday after revelations that his ex-wife had accused him of domestic violence.

Another White House staffer, National Economic Council policy aide George David Banks, also quit after he was told yesterday that he had not cleared a security check due to past marijuana use, according to Politico.

Mr Porter had been operating under a temporary clearance that gave him access to some sensitive information without a final clearance.

The White House has not offered a definitive explanation of when top officials first got word of problems in Mr Porter's background.

The White House has said Mr Kelly asked Mr Porter to resign when he became "fully aware" of the accusations last Wednesday, the same day the Daily Mail published photos showing one of Mr Porter's former wives with a black eye.

The White House was still working on Mr Porter's security clearance at that point, according to White House spokeswoman Sarah Sanders.

However Federal Bureau of Investigation Director Christopher Wray has contradicted that version of events, telling Congress yesterday that the FBI had completed Mr Porter's security clearance background check in July.

Mr Trump has repeatedly defended Mr Porter without expressing sympathy towards domestic violence victims.