WASHINGTON (AFP, BLOOMBERG, NYTIMES) - A White House speechwriter resigned on Friday (Feb 9) after his former wife said he abused her, the second official from President Donald Trump's administration to step down over such accusations in a week.

Deputy White House spokesman Raj Shah said the White House learnt only late on Thursday about allegations against David Sorensen, who worked at the Council on Environmental Quality.

"We immediately confronted the staffer, he denied the allegations and he resigned today," Shah said.

A White House official speaking on the condition of anonymity said Sorensen's position at the White House did not require security clearance, and that his routine background check had been ongoing.

Sorensen's former wife claimed that he was physically and emotionally abusive during their marriage, according to a report in the Washington Post.

The allegations became public just days after former staff secretary Rob Porter resigned amid claims of abuse by two former wives and a former girlfriend.

White House officials have faced criticism for their handling of the Porter episode, after initially offering statements supportive of him.

On Friday, President Trump praised Porter's performance and did not denounce domestic violence in comments to reporters in the Oval Office.

"He did a very good job when he was in the White House and we hope he has a wonderful career, and hopefully he will have a great career ahead of him," the President said.

Trump reminded reporters that "he says he's innocent and I think you have to remember that".

White House chief of staff John Kelly, meanwhile, told officials in the West Wing on Friday that he was willing to step down over his handling of allegations of spousal abuse against Porter, according to two officials aware of the discussions.

The officials emphasised that they did not consider a resignation imminent, and that Kelly - a retired four-star Marine general who early in his tenure often used the threat of quitting as a way to temper Mr Trump's behaviour - had made no formal offer.

In comments to reporters at the White House on Friday, Kelly said he had not offered to resign.