Kelly issued a statement after the allegations were first published by the Daily Mail on Tuesday, vehemently praising Porter as a "man of true integrity and honor".
Trump then highlighted Porter's denial of his two ex-wives' allegations that he struck them while married.
Vice President Mike Pence said he was "appalled" when he first learned about the domestic abuse allegations against now-former White House staff secretary Rob Porter, and is "going to look into the matter" of what the White House and chief of staff John Kelly knew.
"He says he's innocent, and I think you have to remember that", Trump said.
Porter issued a statement midday Wednesday denying the allegations but announcing his departure. It's obviously a tough time for him, ' Trump said.
In remarks at the White House, Mr. Trump wished Mr. "We hope that he will have a wonderful career". He said very strongly yesterday that he's innocent.
And many, including the president himself, have turned their ire on Kelly for vouching for Porter's character and falsely asserting that he had moved aggressively to oust him once his misdeeds were discovered. The fallout from his resignation reverberated amid concerns about his access to classified information and about how long senior staffers had known about the allegations.
Sources told the outlet that both women were considered part of Porter's "dark past" and were cited as reasons why the official was denied security clearances. Porter was even allowed to put out his own statement, quite an accommodation from any employer, never mind the White House, for a reported abuser. The official said White House counsel Don McGahn was apprised of at least some of the accusations at least four times, including in January 2017, the official said.
The president's remarks came on a morning when Porter's second wife appeared on NBC's "Today Show", detailing physical abuse, and saying she gave a full accounting months ago to Federal Bureau of Investigation agents.
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Jonathan Lemire, Catherine Lucey and Jill Colvin are Associated Press writers.
Porter had a temporary security clearance at the White House during his year's work.
White House spokesman Raj Shah is calling the allegations "upsetting" and "shocking". In recent weeks, the president has complained about the chief of staff to his circle of informal advisers, according to two people who speak to the president regularly but are not authorized to publicly discuss private conversations.
Kelly said he took action within 40 minutes of seeing the photos that had surfaced overnight showing one of Porter's ex-wives with a black eye she claims she got because of Porter.
"He said he didn't meddle", Trump said. A Harvard-educated lawyer and Rhodes Scholar, he was one of the few top Trump aides to bring previous executive branch experience. The official White House position is that every last one of these women is lying.
In November, the White House heard back from the Federal Bureau of Investigation.
"White House chief of staff John Kelly must resign", said Van Pelt.
'I think the White House has acknowledged that they could have handled it better, ' he said, distancing himself entirely from the scandal.
Porter's former wives recounted physical, verbal and emotional abuse they say he subjected them to during their marriages.