Seeking to bolster his credentials as an independent candidate, Angus King appointed Republicans, Democrats and independents in equal measure Tuesday to serve as statewide leaders of his campaign for the U.S. Senate seat that’s being vacated by Republican Olympia Snowe.

King announced the selection of three Republicans, three Democrats and three independents as state chairs. Three served in the Legislature while he was governor, and one served in his administration.

“I’m pretty proud that people who worked with me have stepped up. This isn’t easy for a party member. They’re going to take flak from both sides,” King said.

King, a former two-term governor, is the leading independent running for the soon-to-be-vacant Senate seat. Six Republicans and four Democrats are running for their parties’ nominations in June’s primaries.

The Senate now has 51 Democrats, 47 Republicans and two independents, who caucus with Democrats. The National Republican Senatorial Committee accused Democrats and King of cutting a deal behind the scenes in which King would caucus with Democrats if elected.

King said Tuesday that he has had no contact with Senate Democrats. “No telephone calls, no meetings, nothing, nada, zip, nil,” he said.

As for the state chairs, the independents are Eliot Cutler, a 2010 candidate for governor, state Sen. Richard Woodbury and former state Rep. Sherry Huber. The Democrats are former House Speaker Michael Saxl, who said he has never before endorsed anyone outside his party, and former legislators Judy Paradis and Barbara Trafton. The Republicans are 2010 gubernatorial candidate Matt Jacobson and former lawmakers Sue Bell and Jim Libby.

Saxl, Libby and Paradis served in the Legislature while King was governor, and Bell was his senior policy adviser.

King said he had a conference call with four of the state leaders Tuesday, and all agreed that the focus of the campaign should be on uniting Mainers and overcoming partisan gridlock.

“That’s the theme – common sense and problem-solving, not worrying about which color shirt someone has on or which team someone is on,” King said.