Alister Jack also said the Prime Minister was “robbed” by a birthday cake at an event during the partygate scandal.
The prime minister is in a “robust” mood despite Sajid Javid, Rishi Sunak and other ministers leaving the government in the wake of the Chris Pincher affair, Jack said.
He spoke to reporters on Wednesday morning.
The Scottish secretary said: “I am optimistic that the Prime Minister will keep it up.
“The road is bumpy and I’m not going to do anything else. But he has faced challenges before and he has endured.
“He needs, we need a government reset and it will come.”
The Scottish minister said the prime minister had apologized for handling the Chris Pincher affair.
Of the partygate scandal, he said: “He, like Rishi, was robbed by a birthday cake that they didn’t see coming when they were in the cabinet.”
He continued: “They were not at a party, a party arrived and caught them doing it.
“I mean, let’s be honest about that.”
Mr Jack said: “The Metropolitan Police saw the word party after birthday and gave the pair a fixed fine. And that is a fact.”
“But on the other questionnaires, countless questionnaires that he filled out, the Metropolitan Police did not see any parties taking place.”
He said the Prime Minister was not aware of some Downing Street parties, adding: “I think you have to be honest and say, of the events that were work events that he filled out the questionnaires and sent to the police, the police agree that they were work events, and he was not fined.
“And one time, when someone came in with a birthday cake, during a busy day of meetings, he was fined because the word party comes after the birthday.
“So I mean, let’s just put it in some context.”
Asked about the Prime Minister’s mood after the resignation, the Scottish secretary said: “He was in a tough mood, but he absolutely recognizes mistakes made and, as I said, he apologises.”
He said that Rishi Sunak was not mentioned in his conversation with the prime minister.
He added: “He wants to reinstate this government and he was in that frame of mind.”