A businessman unhappy over Sen. Joe Lieberman's support of the Iraq war has gained ground in his primary challenge to the three-term Democrat but remains behind, a poll released Thursday found.

Among all Democrats, 57 percent said they would vote for the moderate Lieberman, compared with 32 percent for Greenwich businessman Ned Lamont, the Quinnipiac University poll found.

A month ago, Lieberman drew 65 percent to Lamont's 19 percent.

Poll director Douglas Schwartz said Lamont is probably benefiting from media coverage of last month's state Democratic nominating convention, where he won 33 percent of delegates.

Lieberman, the Democratic nominee for vice president in 2000, is facing his first primary since joining the Senate in 1988. He has drawn criticism from Lamont and others in his party for advocating the Iraq war and supporting some GOP policies.

In the governor's race, the poll showed Republican Gov. M. Jodi Rell with a 75 percent approval rating and better than 2-to-1 leads over her Democratic challengers, New Haven Mayor John DeStefano and Stamford Mayor Dan Malloy.

The telephone poll of 2,114 registered voters in Connecticut was conducted from May 31 to June 6 and has an error margin of plus or minus 2 percentage points. The survey includes 751 registered Democrats, giving an error margin of 3.5 percentage points.