Carwyn Jones has said he will not set a timetable for standing down as first minister, pledging to "get through the inquiries" launched since the death of former minister Carl Sargeant.
Speaking on a visit to the US, Mr Jones told the BBC he was focused on trying to attract jobs to Wales.
He said he would not copy Rhodri Morgan, who announced retirement plans more than a year before stepping down.
Mr Jones also denied Tory claims Welsh Labour was in "chaos" on Brexit.
The Welsh Labour leader has been first minister since December 2009, when he took over from Mr Morgan.
Asked if he would announce a timetable on his departure, Mr Jones said: "No. I think what you have to do is to carry on.
"From my perspective of course there comes a point where somebody else would step into the role of first minister.
"That's quite natural, but on the moment I'm focused on getting jobs."
The Welsh Government has announced three inquiries since Mr Sargeant was found dead at his home in Connah's Quay, Flintshire, last November.
He had been sacked as communities secretary four days earlier following allegations about improper conduct with women.
One of the inquiries, led by an independent QC, is looking at how Mr Jones handled his dismissal.
"I think it would be quite wrong for anybody to disappear in the middle of that process. That is hugely important," the first minister said.
He said it was "in the nature of politics that people always talk about what's happening next", adding: "But from my perspective it's important to get through the inquiries and get to the end of that process.
"And it's hugely important of course that at some point in the future - whenever that might be - there's a seamless handover."
Mr Jones said he wanted to explore the possibility of a free trade agreement with the US as a "back stop" but he would rather Britain stayed in Europe's customs union.
In a statement issued before his trip began on Monday, the first minister said he would "press the case for developing a free trade agreement between our countries".
But during an interview in New York on Wednesday, he said: "You have to cover all your bases when you're involved in politics.
"But let me be absolutely clear - staying in the customs union is the best way forward for Wales."