New York Rep. Gregory W. Meeks denied Tuesday that he told David A. Paterson — his home state’s embattled Democratic governor — that the Obama White House does not want him to run when his seat is up in 2010.

But Meeks, a House veteran from the New York City borough of Queens, was vague on the specifics of the conversations he did have with Paterson.

Meeks commented on the situation while making the New York media rounds in the wake of a story published Sunday by the New York Times. That article said President Obama and his political team wanted Paterson to step aside, and asked Meeks, who is close to both men, to deliver the message.

Paterson has suffered from a sharp decline in his approval ratings since March 2008, when he moved up from lieutenant governor to succeed resigned Democratic Gov. Eliot Spitzer, and many Democrats worry that his determination to seek a full term in his own right next year could cost his party the seat.