Caroline Kennedy, daughter of the late President John F. Kennedy, was making calls Monday to prominent Democrats in a bid to be considered for the Senate seat of Secretary of State-designate Hillary Rodham Clinton , D-N.Y.

And it didn’t take long for her to secure a coveted endorsement — that of House Rules Committee Chairwoman Louise M. Slaughter .

“Caroline Kennedy understands that the stakes have never been higher for our state and our nation. We need our next senator to have the skills and the stature to help bring about the change we need,” Slaughter said.

The 11-term incumbent added, “I am anxious to work with Caroline Kennedy on the needs of upstate New York should Governor Paterson choose to appoint her to the Senate.”

New York congressional aides confirmed that Kennedy has made calls to several prominent Democrats in the New York House delegation expressing her interest in the post. Both the Associated Press and New York Times report that she also has spoken to Paterson about her desire.

It will be up to Paterson to choose someone to fill the Senate seat until 2010, when a special election will be held for the remainder of Clinton’s second Senate term. She won re-election in 2006 with 67 percent of the vote.

Kennedy spoke to the governor earlier this month about the seat, but took a few weeks to decide that she would seek appointment.

Paterson’s office did not return a request for comment, nor did Kennedy’s.

Paterson has said he will not make an appointment until Clinton’s confirmation process is completed in January.

A wide array of state-based political leaders and members of Congress have expressed interest in the seat, but Kennedy’s star power makes her a frontrunner.

Her embrace of the political spotlight is something new for Kennedy, who has avoided the media glare for most of her adult life. It was not until her high-profile endorsement of President-elect Barack Obama during the contentious Democratic primary last spring that Kennedy chose to assume a more public role in politics.

In seeking the Senate seat, Kennedy will be aided by the vocal backing of her powerful family, including Massachusetts Sen. Edward M. Kennedy .

New York City Mayor Michael Bloomberg, a former Republican turned independent, and Obama have both spoken favorably of Caroline Kennedy in recent weeks as well.