DeLay stepped stepped down as House majority leader in the fall after he was indicted on state money laundering charges in Texas.
In letters sent Saturday to fellow House Republicans and Speaker J. Dennis Hastert, DeLay said he supported the call for an election of a new leader, The New York Times reported.
"The job of majority leader and the mandate of the Republican majority are too important to be hamstrung, even for a few months, by personal distractions," DeLay said in the letter to Hastert.
Hastert said Republicans would hold a leadership election after they return for the State of the Union address on Jan. 31.
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