The Chancellor’s comments followed weekend reports suggesting he backed Boris Johnson for the party’s top job in the aftermath of this year’s disappointing election result.
Mr Hammond also warned that the prospect of income tax rises in Scotland, which First Minister Nicola Sturgeon is now actively considering, could hit hard-pressed families in the pocket.
He was in Scotland on Monday to announce a new £5 million fund to boost North Sea exploration and meet business leaders in the North-east.
But while he backed Mrs May to lead the UK through the Brexit process, he would not endorse the Prime Minister to lead the party into the next election.
“I’m not going to get involved in the discussion about future Conservative party leadership politics,” he said.
“Theresa May made it very clear that she has a job to do. I’m completely behind her in doing that job – she’s making an excellent job of managing the Brexit negotiations.
“We’re entering a critical phase now and all of us need to focus our attention on delivering a Brexit that works for Britain.”
He insisted next week’s Tory party conference will show that the party is “clear and unified” around Theresa May delivering a Brexit that “works for Britain.”
“That’s going to be our primary focus.”
The party is preparing to head to Manchester at the weekend for its autumn conference after weeks of reports of turmoil over Brexit divisions and claims of jockeying for position to succeed Mrs May.
According to weekend reports, Mr Hammond texted the Foreign Secretary at 4am the morning after the election to offer his support for a leadership run under a deal where he remained Chancellor. Mr Hammond said he did “not recognise” some of the material” which appeared. He said that after Mrs May got in touch inviting him to serve in her government he “committed to do so and to back her”.
Pressed again about the Prime Minister leading the Tories into the next election, Mr Hammond added: “I’m not going to talk about future Conservative leadership, I want to talk about the job in hand.
“Theresa May is clearly the best person to lead the Conservatives, to lead the government through this very complex process of Brexit and that’s what she’s focused on. She’s been very clear that that’s the job in hand, that’s the job that she considers she was elected to do and she’s going to get on with it.”
He added that the next election is “not issues for today”.
Ms Sturgeon has commissioned research into the prospect of income tax hikes next year and is now open to this as a means to boost public spending.
The Chancellor accepted devolution means it is up to the Scottish Parliament to make this decision and said it was a “perfectly legitimate debate for the people of Scotland to have.”
But he added: “Personally, I think one should be cautious at a time of uncertainty. And there is uncertainty created by the Brexit process itself, there’s uncertainty created by the pressure on real incomes from the spike in inflation following the currency depreciation last year. I think one should be cautious about increasing the pressure on household incomes through taxation at a time like this.”