In a statement to Britain's domestic Press Association news agency on Friday, Gilligan conceded that part of his 29 May report - which alleged that Downing Street "sexed up" intelligence on Iraq - was wrong.
"I again apologise for it," he said. "My departure (from the BBC) is at my own initiative. But the BBC collectively has been the victim of a grave injustice.
"I love the BBC and I am resigning because I want to protect it. I accept my part in the crisis which has befallen the organisation. But a greater part has been played by the unbalanced judgments" contained in Lord Brian Hutton's report into Kelly's death, he said.
Following the leaders
Gilligan's resignation came after the stepping down of both the BBC chairman and the director general following Hutton's inquiry that slated the British broadcaster.
Hutton's report on Wednesday criticised Gilligan, the BBC's management and its supervisory board of governors.
Hutton said the BBC report was unfounded. He said the BBC's editorial system was "defective" in allowing Gilligan's report to air and the governors should have investigated it in the aftermath, during which Kelly was unmasked as Gilligan's source.