Los Angeles ? Only about a third of Democratic Party insiders think former Vice President Al Gore should run for president again in 2004, according to a poll published Sunday.

The Los Angeles Times poll of 312 Democratic National Committee members – roughly three-quarters of the committee’s total membership – suggests the contest is wide open, with none of the top possible candidates standing out as having particularly broad support.

A poll released Sunday, by Time and CNN, shows that just over a third of Americans think there is a Democrat who can defeat President Bush in 2004, and half think there is not.

Among Democrats and those leaning Democratic in the general population, 36 percent in the Time-CNN poll favored Gore, while 26 percent said they would support Sen. Hillary Rodham Clinton. Clinton aides have said she is not planning to run in 2004. All other potential candidates were in single digits.

The poll of 474 Democrats or those who lean Democratic was conducted Wednesday and Thursday. It had an error margin of plus or minus 5 percentage points.

Only 35 percent of the DNC members polled for the Los Angeles Times said Gore should run again, while 48 percent said he should not and 17 percent were undecided.

Asked who they favor in the 2004 race, 46 percent of the respondents said they had no preference. Out of a list of 10 prospective candidates, 19 percent of those polled named Gore as their pick, 18 percent backed Sen. John Kerry of Massachusetts, and 13 percent named Sen. John Edwards of North Carolina.

Rep. Richard Gephardt of Missouri, the outgoing Democratic leader in the House, was chosen by 10 percent. The other possible candidates were in single digits, including Sen. Joseph Lieberman of Connecticut, the 2000 vice presidential nominee, who garnered 4 percent.

The poll found that party insiders still have great affection for former President Clinton. Ninety-six percent of those polled said they viewed Clinton favorably.

The telephone poll, conducted from Nov. 7 through Thursday, had a sampling error margin of plus or minus 2 percentage points.