Dodd, who was given the job of general chairman of the Democratic National Committee by Clinton's husband, expressed concern about a prolonged nomination fight that could be "highly divisive" and "highly detrimental" to the party's chances of winning the presidency in November.
Now is the time for the party "to come together," said Dodd, who said he was not calling on Clinton, who had also sought his endorsement, to quit the race.
Recent polls show the race tightening in Ohio, with Clinton still holding a slight lead. The latest statewide survey in Texas, by Opinion Research Corporation for CNN, showed Obama pulling ahead in that state.
Obama also leads Clinton by a significant margin in the latest national surveys, including a New York Times/CBS poll that showed him with a 16-point lead and a USA Today/Gallup survey that put him 12 points ahead.
A memo by Clinton's chief strategist, Mark Penn, released last night to reporters, indicated that her nomination chances depend on demonstrating "momentum" and convincing voters that she is "ready to take on John McCain."
Recent polling has shown Obama outperforming Clinton in test matches against McCain, with Obama either ahead of or even with McCain.
However, a national poll released last night showed McCain running ahead of either Democrat. The Los Angeles Times-Bloomberg survey showed him leading Obama by 44 percent to 42 percent, within the poll's 3-point margin of error, while Clinton would lose by 6 percentage points, 46 percent to 40 percent.