Mr Geithner had previously said the deadline for a deal was 8 July.
But in a letter to Congress he said that better tax receipts meant the deadline could be extended to 2 August.
Republicans want to tie any agreement on the US budget to spending cuts, especially in the healthcare programme.
The Obama administration has proposed a $4tn package of budget cuts, but the Republicans say they do not go far enough.
Despite pushing back the deadline, Mr Geithner nevertheless warned Congress of the need for a urgent resolution to the impasse.
He said in his letter: "While this updated estimate in theory gives Congress additional time to complete work on increasing the debt limit, I caution strongly against delaying action."
Last month, ratings agency Standard & Poor's warned that the failure to agree a budget deal was damaging the financial credibility of the US.
In a surprise move, which hit share prices on both sides of the Atlantic, S&P downgraded its US credit rating outlook from stable to negative, increasing the likelihood that the rating could be cut within the next two years.
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