The Cabinet Office inquiry also found that the claims made by Kate Maltby, the Conservative activist who claimed Green had made unwanted sexual advances towards her, were "plausible".
"I share the concerns that have been raised by police, and I expect those issues be properly investigated", May said in a press conference during her visit to Poland.
He maintains that he did not download or view porn in the House of Commons, but accepted he had not been clear about whether police had spoken to him about it or not.
A report by May's Cabinet secretary concluded Green had made misleading statements regarding his knowledge about the indecent images found by police. The pornography was found on his office computer during a police investigation of government leaks.
But Mr Hunt suggested Mr Green had been "pushed into a situation" where he said something he "didn't mean to say".
Mr Quick told the BBC he will continue to "seek a retraction" of the comments Mr Green made about him, saying the matter was "in the hands of my lawyers".
Miss America leadership resigns in email shaming scandal
The writer responded by questioning whether he and Haskell were part of a tiny group of people who had not had sex with Hagan. Elizabeth Gracen, an Arkansan who won the competition in 1982, also signed her name to petition.
The Metropolitan Police, who referred the case to the data regulator, said the pair were under investigation over the "apparent disclosure to the media of confidential material gathered during a police investigation in 2008".
The health secretary was asked by BBC Radio 4′s Today programme on Thursday morning to drop the pretence that Green resigned and was in fact sacked. He was found to be in breach of the ministerial code.
Sources close to Mr Davis said he had warned Downing Street against sacking Mr Green but in the aftermath of his forced resignation, sources close to the Brexit Secretary said he would not be resigning in protest.
Hunt, who has been named as a possible successor to Green as first secretary of state, added: "Clearly he did something that was a breach of the ministerial code and that's why Theresa May took the decision that she did".
Asked if his departure left Theresa May more isolated, Mr Hunt said "leadership is lonely" but she had shown "extraordinary resilience in very challenging circumstances".
"We have received many supportive messages from people near and far who appreciate Kate's courage and the importance of speaking out about the abuse of authority".