With most of the votes in, Lieberman continued to run about 4 points behind Lamont, The New York Times reported.
But Lieberman told a cheering crowd that he plans to remain in the Senate. He has filed to run as an independent in November.
The primary had turned into a referendum on the war in Iraq, with Lamont portraying Lieberman as a staunch supporter of President Bush. But polls showed the race tightening as the primary approached.
Lieberman appears to have a good shot at winning the second round. A recent Quinnipiac University poll showed him winning a three-way race with just over half the vote.
Lamont, 52, a cable television entrepreneur descended from Morgan partner and philanthropist Thomas Lamont, shrugged off poll numbers in his challenge of the three-term, 64-year-old Lieberman, predicting his own victory, the Times reported.
"On Aug. 9 we're going to have a lot of new best friends," Lamont said.
The contest turned nasty in its final hours. When Lieberman's Web site went down, his staff accused Lamont's supporters of sabotage while Lamont's staffers suggested Lieberman had forgotten to pay the bill, the Times said.