CHARLESTON, South Carolina — US Republican presidential candidate Michele Bachmann said Wednesday she has no plans to stoop to a "mud-wrestling fight" between her and fellow arch-conservative Sarah Palin.

Bachmann, on the campaign trail in the state of South Carolina two days after officially launching her 2012 White House run, accused the media of seeking to pit the two women against one another by suggesting there was no room in the race for two female Tea Party movement favorites.

"I have a very good relationship with Governor Palin," Bachmann said in response to a question from the audience at a public park in Charleston.

"This seems to be their sideline right now," she said of the media.

"They want to see two girls come together and have a mud-wrestling fight. And I'm not going to give it to them because I have great respect and admiration for the governor," Bachmann said, referring to Palin who was the governor of Alaska and has been mulling a Republican presidential run.

Bachmann, a US congresswoman from Minnesota, has drawn American media attention this week after her strong poll numbers in the heartland state of Iowa, home to a first-in-the-nation caucus that shapes the Republican presidential field.

Palin, the 2008 Republican vice presidential nominee, has not announced if she will run for president. But she too was in Iowa this week, ostensibly to attend the premier of a documentary movie about her political life.