WASHINGTON (Reuters) - Treasury Secretary Timothy Geithner warned on Wednesday that "prioritizing" government payments to avoid a debt default would spur deep cuts in other disbursements and still cause investors to shun Treasury securities.

In a letter to senior Republican senators, Geithner said their proposal to keep the debt limit at the current level while ensuring payment of interest on the federal debt is unworkable.

"Ultimately, the notion of 'prioritizing' payments is futile because the debt limit must be increased regardless of which spending path is adopted," Geithner wrote. "There is no credible budget plan under which a debt limit increase can be avoided."

(Reporting by David Lawder; Editing by James Dalgleish)