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".
"But clearly he did something that was a breach of the ministerial code and that's why Theresa May took the very hard decision that she did".
Last month, the Sunday Times broke the story that police claimed to have found "extreme" pornographic material on Green's House of Commons computer.
The Prime Minister called on Mr Green, a lifelong friend, to quit his role as the de facto deputy prime minister after he made "misleading" statements about allegations that police found pornography on computers in his office in 2008. An investigation was launched by the cabinet secretary, and it was determined that Green did not adhere to the "seven principles of public life"-one is honesty-as required by the ministerial code".
Besides allegations that he kept and watched pornography on his parliamentary computer, Green faces another allegation from writer and Tory activist Kate Maltby.
"I'm sure she didn't want him to go", Hunt said.
Bristol City dump holders Man Utd out of League Cup
Of course we don't want extra-time, of course we try to win the game in the 90 minutes - which is why I say they were lucky. Here's video of the game victor , scored by Korey Smith in the third minute of extra time. "A lovely day for football".
Maltby said Green had "fleetingly" touched her knee during a meeting in a pub and later sent a suggestive text after a picture of her wearing a corset appeared in a newspaper.
"It is therefore with deep regret, and enduring gratitude for the contribution you have made over many years, that I asked you to resign from the Government and have accepted your resignation".
The letter also said Mr Green, 61, "recognised" he made a female journalist "feel uncomfortable".
Mr Hunt continued: "He lied on a particular incident, yes, I think lots of people who understand the context would appreciate why that might have happened but that doesn't make it any Cabinet ministers to the very highest standards of conduct, rightly, but I think we should remember that those are standards that would probably not apply in many other countries".
Ms Maltby is not commenting on Mr Green's resignation until she receives more details from the Cabinet Office.
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