With six weeks to go until the June 5 primary, a new poll suggests that it's a three-man race to be the next governor of California.

A poll of 520 likely primary voters released by SurveyUSA and sponsored by KABC-TV Los Angeles, KFSN-TV Fresno, KGTV-TV San Diego, KPIX-TV San Francisco and the San Diego Union-Tribune found that Gavin Newsom, Antonio Villaraigosa and John Cox are all within 6 percentage points of one another.

Newsom led the field with 21 percent of the vote, but was followed closely by fellow Democrat Antonio Villaraigosa with 18 percent. Republican John Cox came in third with 15 percent, and was followed by fellow Republican Travis Allen at 10 percent and Democrat John Chiang at 9 percent.

RELATED: Gavin Newsom says alcohol isn't a problem anymore: 'A little wine' is fine

No other candidate received more than 5 percent support; 17 percent of the poll's participants were undecided.

Now Playing:

Six leading candidates for California governor agreed that it's too hard to build new homes in California and offered wide ranging solutions to rein in exploding housing costs and rising homelessness. The candidates spoke separately Thursday at a housing conference in Sacramento. For decades, California has failed to build enough homes to meet demand, particularly in popular coastal cities such as San Francisco.

Media: KCRA

The top two finishers in the June 5 primary will go on to face each other in the November general election, regardless of political party.

The poll also found that 66 percent of Californians support sending troops from the California National Guard to the Mexican border. 30 percent of participants said they support sending troops to "patrol for people attempting to cross the border illegally," and an additional 36 percent said they support sending troops to the border as long as they "only focus on gang and drug activity."

MORE: John Cox's interview with Laura Ingraham goes off the rails after guest insults Cox, Ingraham

Just 27 percent of the poll's participants said that National Guard troops shouldn't be sent to the border, while 7 percent were undecided.

In the Senate race, the poll found that Dianne Feinstein maintains a large lead over her many primary challengers.

Feinstein leads the way with 39 percent, and the next closest contender is Republican Patrick Little, with 18 percent. State Senate leader Kevin de León garnered just 8 percent support.