The survey by Franklin Pierce College (search), conducted April 27-May 1, found the two candidates at 23 percent, with Sen. Joe Lieberman of Connecticut far behind at 9 percent and Rep. Dick Gephardt of Missouri at 8 percent.
The results were similar to a survey by the same organization in early April. A Mason-Dixon (search) poll released this weekend, however, showed Kerry at 28 percent and Dean at 21 percent.
Beyond the support numbers in the Franklin Pierce poll, Kerry had a favorable rating of 64 percent, the highest of the Democrats, and just 4 percent didn't know the Massachusetts senator. Dean had a favorable rating of 49 percent and 18 percent did not know about the former Vermont governor.
The poll of 600 likely primary voters had an error margin of plus or minus 4 percentage points.
The competition between Dean and Kerry has been fierce, with the two candidates and their respective campaigns at odds over a number of issues, including national security, the U.S.-led war against Iraq and the long-term strength of the U.S. military.
In the poll, two Democrats who have not announced -- former Colorado Sen. Gary Hart and retired Gen. Wesley Clark -- were at 2 percent. Democrats who are running for president -- North Carolina Sen. John Edwards, Florida Sen. Bob Graham, Ohio Rep. Dennis Kucinich and former Illinois Sen. Carol Moseley Braun -- were at 1 percent and Al Sharpton was at 0 percent.
Almost a third of those surveyed, 31 percent, were undecided, down from 38 percent in the early April poll.