Senator Hillary Rodham Clinton, a longtime supporter of Senator Joseph Lieberman, said Tuesday she will not back the Connecticut Democrat's bid for re-election if he loses their party's primary. "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." There was no immediate comment from Lieberman. 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 August 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 US troops despite her criticism of President George W. 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," Clinton said in her statement of Tuesday. Democrats hoping to win back the Senate have been looking to win seats in states such as Pennsylvania, Montana, Missouri, Virginia and Tennessee, and Lieberman's decision to begin collecting the 7,500 signatures needed to assure a separate spot on the November ballot could complicate things. Both Senate Democratic Leader Harry Reid of Nevada and Senator Charles Schumer of New York, 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.