"I've known Joe Lieberman for more than thirty years. I have been pleased to support him in his campaign for re-election, and hope that he is our party's nominee," the former first lady said in a statement issued by aides.
"But I want to be clear that I will support the nominee chosen by Connecticut Democrats in their primary," the New York Democrat added. "I believe in the Democratic Party, and I believe we must honor the decisions made by Democratic primary voters."
Asked about Clinton's comment, Lieberman spokeswoman Marion Steinfels said the three-term senator was "totally focused on winning the Democratic primary."
"Senator Clinton and President Clinton have both been supporters of Senator Lieberman for many, many years. He greatly values her friendship and her support in the primary," said the Lieberman aide. "The support is part of the reason he's working so hard, with a single-minded focus to win the Democratic primary."
Facing a stronger-than-expected Democratic primary challenge from millionaire businessman Ned Lamont and sagging poll numbers because of his support of the Iraq war, Lieberman said Monday he'll collect signatures to assure an independent ballot spot for the November election if he loses the Aug. 8 primary.
The move has complicated life for Lieberman's fellow Senate Democrats, including Clinton, who has been under attack from some Democrats for her own vote to authorize the Iraq war and her continuing refusal to back a specific timetable for the withdrawal of U.S. troops despite her criticism of President Bush's handling of the conflict.
"The challenges before us in 2006 call for a strong, united party, in which we all support and work for the candidates who are selected in the Democratic process," said Clinton's Tuesday statement.
National polls have Clinton as the front-runner among potential 2008 Democratic presidential contenders. Lieberman was the party's vice presidential candidate in 2000 when Bush defeated then-Vice President Al Gore to win the White House.
Democrats hoping to win back the Senate have been looking to win seats in states such as Pennsylvania, Montana, Missouri and Tennessee, and Lieberman's decision to begin collecting the 7,500 signatures needed to assure a separate spot on the November ballot could add complications.
Both Democratic Senate Leader Harry Reid, D-Nev., and U.S. Sen. Charles Schumer, D-N.Y., chairman of the Democratic Senatorial Campaign Committee, said they are backing Lieberman in the primary.
"We aren't going to speculate about what happens next because that would undermine our candidate," said DSCC spokesman Phil Singer.
Senator Joe Biden, D-Del., along with Senators Barbara Boxer, D-Calif., and Ken Salazar, D-Colo., are also supporting Lieberman and plan to campaign for him between now and the primary.
Meanwhile, the Boston Globe reported that Senator John Kerry, D-Mass, has declined to endorse either Lieberman or Lamont in the primary.
Clinton faces a possible September primary in her own re-election race this year from an anti-Iraq war activist. Jonathan Tasini is seeking the signatures of at least 15,000 New York Democrats to force a Sept. 12 primary.