AUGUSTA, Maine — A new poll out Thursday shows independent Angus King holding a 12-point lead over Republican rival Charlie Summers in the race for Maine’s open U.S. Senate seat.

In the poll, the first of the Maine Senate race conducted by Rasmussen Reports, King attracted the support of 45 percent of respondents, Summers had 33 percent support and Democrat Cynthia Dill had the support of 14 percent of those surveyed.

Another 1 percent of those polled said they preferred another candidate while 7 percent said they were undecided.

Rasmussen Reports polled 500 likely voters on Sept. 25. The survey has a margin of error of 4.5 percent.

The firm’s Maine Senate poll asked voters only about King, Summers and Dill by name. The race also features three other candidates: independents Danny Dalton, Andrew Ian Dodge and Steve Woods.

The Rasmussen results aren’t far off from the results of a Public Policy Polling survey published last week that showed King with 43 percent support, Summers with 35 percent and Dill with 14 percent. Eight percent were undecided in that survey.

While Public Policy Polling was founded by Democratic pollster Dean Debnam, Rasmussen Reports founder Scott Rasmussen has built up a reputation for publishing surveys with results that lean Republican and are touted by Republicans.

In the presidential race, Rasmussen’s daily tracking poll on Wednesday showed President Barack Obama and former Massachusetts Gov. Mitt Romney tied while most other recent polls showed an edge for Obama.

Public Policy Polling and Rasmussen Reports both conduct their polls using automated telephone surveys that use a technology known as Interactive Voice Response. In polling the Maine Senate race, both firms also asked only about King, Summers and Dill by name.

The firms differed, however, in sample size: Public Policy Polling surveyed 804 likely voters to Rasmussen’s 500. And the firms have differences when it comes to calculating results.

According to its website, Rasmussen “weights” results by political party, so if the percentage of respondents who say they are Democrats is greater than the percentage of voters registered as Democrats, the pollster adjusts results accordingly.

Thirty-five percent of Rasmussen’s respondents identified themselves as Democrats, 30 percent as Republicans and 35 percent as “other.” According to the secretary of state’s office, 33 percent of Maine’s voters were registered as Democrats, 28 percent as Republicans and 36 percent unenrolled in November 2011.

Public Policy Polling doesn’t adjust results based on party identification. In its survey, 42 percent of respondents said they were Democrats, 29 percent Republicans and 29 percent independents.

If Rasmussen’s Maine Senate survey leans Republican, the results could be good news for King, who has seen his lead shrink in the Senate race since June as outside groups with Republican ties have funneled nearly $2 million into ads attacking the former governor.

The Portland-based Maine People’s Resource Center also released a poll last week that showed King with 44 percent support, Summers with 28 percent and Dill with 15 percent. Seven percent were undecided, and a combined 6 percent chose independents Woods, Dodge or Dalton.

The resource center — which is affiliated with the left-leaning Maine People’s Alliance, a statewide advocacy group — didn’t weight results by political party and asked respondents about all six Senate candidates by name.

The Rasmussen survey also found 47 percent approval and 51 percent disapproval for Gov. Paul LePage’s job performance, notably higher ratings for the Republican governor than last week’s surveys. Public Policy Polling found 37 percent approval and 52 percent disapproval, while the Maine People’s Resource Center found 39 percent approval and 54 percent disapproval.