The heavy losses for Labour in the May 7 elections triggered almost a quarter of his MPs to call for him to go, and two rivals are openly vying to replace him, unsettling investors who have pushed up the government's borrowing costs.
"I am focused on the job that I was asked to do, which is to serve my country and to carry out my duties as prime minister of this country," he told staff during a visit to the Labour Party's headquarters on Monday.
Earlier, Deputy Prime Minister David Lammy said Starmer would not be setting out a timetable for his departure.
This came after media reports over the weekend said he was weighing whether or not to announce a plan to step down.
Wes Streeting, who quit as health minister last week, said on Saturday he would stand in any formal leadership contest.
Greater Manchester Mayor Andy Burnham is seeking a seat in parliament that would allow him to make a challenge too.
Starmer has repeatedly said that he intends to fight any leadership challenge.
Any candidate wishing to make a challenge would need to secure the support of 20 per cent of Labour members of parliament.
With Labour currently holding 403 seats, that equates to 81 backers.
