WASHINGTON — White House officials conceded Thursday that they regretted the way they handled accusations against Rob Porter, the staff secretary who resigned Wednesday after two former wives publicly accused him of abusing them. But they refused to provide any information about when President Trump’s most senior advisers first learned about the episodes.

Mr. Porter abruptly departed the West Wing on Thursday afternoon, one day after John F. Kelly, the chief of staff, and other senior officials had issued statements defending him and said they would prefer that he remain in his post.

Among the questions he left behind was whether Mr. Kelly and other members of Mr. Trump’s inner circle had been willing to ignore accusations of domestic violence to protect a trusted aide. Raj Shah, the deputy White House press secretary, said that Mr. Kelly had not been made “fully aware” of them until this week. But two people close to the White House said that Mr. Kelly and Joe Hagin, the deputy chief of staff for operations, as well as Donald F. McGahn II, the White House counsel, had known of the issues since late fall.

It was unclear whether they knew the extent of the women’s allegations, though one former senior American official said that White House officials had been aware in August that the issue was preventing Mr. Porter from obtaining the security clearance he was seeking. Mr. Shah said that Mr. Porter had been operating with an “interim clearance,” which is customary for top White House officials to receive while the F.B.I. conducts a thorough check of their backgrounds.