BRUNSWICK, Maine — Former Gov. Angus King, the presumed front-runner in the race to replace Olympia Snowe in the U.S. Senate, said Wednesday he’ll discourage spending by outside groups on his behalf if his opponents do the same.

King, who is running as an independent, called such spending “a tidal wave of anonymous campaign expenditures that distort our political process.”

He said he sent a letter to the other Senate candidates this morning challenging them to condemn this spending, too.

In Massachusetts, Sen. Scott Brown, a Republican, and his Democratic challenger Elizabeth Warren reached such an agreement.

Under federal election law, candidates are not allowed to coordinate with third-party groups, so Brown and Warren had to find a innovative way to discourage spending by these independent political action committees.

Called the “People’s Pledge,” the pact requires that a candidate who benefits from a third-party ad has to pay a penalty. The money goes to a charity chosen by the other candidate.

In a letter they wrote to third-party groups earlier this year, Warren and Brown said: “Your spending will damage the candidate you intend to help.”

The pledge is credited with helping improve the tone of the Massachusetts Senate race.

While voters said they liked the pledge for curbing nasty attacks, the outside groups said they saw the pledge as an impingement on their speech rights.

Republican strategist Todd Domke told NPR: “At some point [independent groups] will probably say, ‘Forget the People’s Pledge … We’re people, too. It’s time to go to war.’”

In November 2010, the Republican State Leadership Committee spent $400,000 on fliers and ads in five Maine state Senate races. Many of the Republican candidates said they disapproved of the spending on their behalf.

In February, the Maine Ethics Commission fined the committee $26,000 for failing to file timely and accurate reports about the expenditures. It is the largest fine in the agency’s history.

Ultimately, the commission determined that the late filings delayed $160,000 in matching payments through Maine’s public campaign financing program to the targeted Democrats, all of whom lost their campaigns to GOP opponents. Those GOP victories also helped Republicans gain control of the Senate.