While former Mass. Gov. Mitt Romney remains the preferred 2012 Republican presidential nominee, three rivals are close behind -- including two who haven’t announced they are running.

In a Fox News poll released Wednesday, Romney received the backing of 18 percent of GOP primary voters. He’s followed by Texas Gov. Rick Perry at 13 percent, Minnesota Rep. Michele Bachmann at 11 percent and former New York City Mayor Rudy Giuliani at 10 percent. Perry and Giuliani have not declared their candidacies.

Former Alaska Gov. Sarah Palin, also undeclared, is now in single digits at 8 percent support, and Texas Congressman Ron Paul garners the support of 7 percent.

All other candidates receive the support of 5 percent or less.

Click here for the poll results.

Romney officially announced his run on June 2, and Bachmann announced that she had filed the paperwork to run during a Republican presidential debate in New Hampshire on June 13.

In the new poll, Romney’s support dropped 5 percentage points from 23 percent in early June. Since then, Bachmann’s support almost tripled from 4 percent to 11 percent, while Palin’s support dropped 4 points. Perry makes his Fox News poll debut very near the top of the field.

The poll also asked Republican primary voters their second choice. If Giuliani decides against running in 2012, most of his backers would move to Romney, with the rest of the field mostly unchanged.

Palin supporters splinter when asked their second choice, with many undecided. Without Palin in the race, Romney increases his edge by 2 points, and Perry, Bachmann and Giuliani all gain 1 point each.

If Perry decides not to run, Bachmann gets a 5-point bump and Romney gains 2 points.

The Fox News poll is based on landline and cell phone interviews with 912 randomly chosen registered voters nationwide, including 324 GOP primary voters. It was conducted under the joint direction of Anderson Robbins Research (D) and Shaw & Company Research (R) from June 26 to June 28. For the total sample, it has a margin of sampling error of plus or minus 3 percentage points.

Sarah Palin is a Fox News contributor.