DES MOINES, Iowa (Reuters) - The Democratic presidential race in Iowa is a virtual three-way tie between John Kerry, Howard Dean and Richard Gephardt four days before the state's caucuses, according to a Reuters/MSNBC/Zogby poll released on Thursday.

In the latest rolling three-day poll, Kerry registered 21.6 percent with Dean and Gephardt both at 20.9 percent. North Carolina Sen. John Edwards gained two percentage points to 17.1 percent, well within the poll's margin of error, putting all four top contenders in a statistical tie.

"It's a 3-way tie, and Kerry and Gephardt are now tied among union voters as Dean's labor support slips," Zogby said. With Edwards continuing to gain ground "this race is actually a four-way statistical dead heat.

"We might see these candidates exchanging leads all the way to the end," Zogby said, with 11 percent of likely caucus-goers still undecided and many switching their support as they take a harder look at the choices ahead of Monday's contest.

All of the candidates plan an extensive schedule of campaigning in Iowa in the race's final days. Dean and Gephardt have been exchanging heated attacks in the race to the finish.

The rolling poll of 502 likely caucus-goers was taken Monday through Wednesday and has a margin of error of 4.5 percent. The poll will continue each day until Monday's caucuses.

The polling was concluded before Wednesday night's news that former Illinois Sen. Carol Moseley Braun would drop out of the race and throw her support to Dean. Braun's move leaves eight Democrats vying for the right to challenge President Bush in November.

Dean and Gephardt have battled back and forth for months for the top spot in polls in Iowa, the first big contest in the nominating race, but the late charges by Edwards and Kerry, a senator from Massachusetts, have scrambled the Democratic picture.

Dean, the former Vermont governor, still holds a large but shrinking lead over retired Gen. Wesley Clark in polls in New Hampshire, which has a Jan. 27 primary one week after Iowa.

Gephardt, the congressman from neighboring Missouri who won Iowa during his first presidential bid in 1988, must win Iowa to remain in the race.

Clark and Ohio Rep. Dennis Kucinich were at 3 percent in the latest poll, while Connecticut Sen. Joseph Lieberman and Braun were at 1 percent, with former civil rights activist Al Sharpton at less than 1 percent.

Clark and Lieberman are not competing in Iowa.

Polling in Iowa is complicated by the unique nature of the caucus system, which requires participants to leave their homes on a typically bitter cold night and gather with neighbors for hours before publicly declaring their support for a candidate.