It comes as the foreign secretary met with eight of his foreign counterparts at his country residence in Kent over the weekend.
Mr Hunt said: “Challenged a few of my fellow foreign ministers to navigate the Chevening maze in the rain… by comparison to which Brexit discussions seem more straightforward.”
Speaking from the reception in Kent, he said: “I think what we’re reading is that we’ve made a lot of progress. There are still some big issues to settle. We are putting everything into trying to resolve these issues.”
Mr Hunt said that Brexit Secretary Dominic Raab was taking part in “last-minute talks” to try to see if progress could be made on outstanding issues and this was a sign of “how much effort we are putting in.”
The surprise talks come before a key meeting of EU leaders on Wednesday, with the government admitting there are “big issues still to resolve.”
Reuters reported ambassadors for all EU member states, excluding Britain, were summoned to a meeting on Brexit.
When asked if it was now time for the Prime Minister to rethink her strategy, particularly involving discussions on the Irish border, Mr Hunt said: “Theresa May has been absolutely clear that she would not sign up to indefinite membership of a customs union so what we need to do is find a backstop solution that respects her commitment to be leaving the customs union but also satisfies Irish concerns that we would never return to the Troubles.”