"We didn't cover ourselves in glory in terms of how we handled that," Kelly told reporters, although he denied earlier reports that he had offered Trump his resignation.
Kelly was criticised for appearing to side with Porter when the abuse allegations first surfaced and again after the Federal Bureau of Investigation contradicted the White House's initial timeline of events.
The FBI said it completed an investigation into Porter's background in the summer of 2017 as part of the security-clearance approval process and had sent those findings to the White House.
But Kelly insisted on Friday that he did not learn of the abuse allegations against the White House staff secretary until Feb. 6, when an allegation by one of the women was about to surface in media reports.
Kelly and other White House officials initially defended Porter, who has denied the allegations.
Kelly said on Friday he at first believed Porter was involved in no more than a "messy divorce" but that he made clear that Porter had no choice but to resign when he learned later on Feb. 6 that another former wife had accused Porter of physical abuse.
White House spokeswoman Sarah Sanders continued to defend Porter into the following day and initially said Porter did not resign until Feb. 7, something Kelly called a "mixup." Porter was seen working at the White House that day.
Porter, as White House staff secretary, helped Kelly manage the flow of information that reaches the president daily.
On Feb. 13, FBI Director Christopher Wray testified before Congress that the agency completed its background check of Porter in July 2017 and had sent material on Porter's past to the White House as early as that March.
The FBI was asked to provide additional findings, which it sent to the White House in November and then again last month.
Still, Kelly said that "we had not reached endgame" in the case and that Porter's security clearance was pending until the abuse charges came to light.
"It was just a shock to us all," Kelly said.
(Reporting by James Oliphant; additional reporting by Steve Holland; editing by Grant McCool)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)