AUGUSTA, Maine — Former Gov. Angus King turned in more than 5,800 signatures Tuesday to qualify for November’s ballot as a U.S. Senate candidate.

Ten campaign volunteers who collected the most signatures for the ex-governor accompanied King to the secretary of state’s office in Augusta to submit the petitions. King needs 4,000 valid signatures to qualify as an independent candidate in the race to replace Republican Sen. Olympia Snowe, who announced in late February that she wouldn’t seek re-election.

King’s campaign said volunteers collected about 6,400 signatures from voters in every Maine county. State law allows the campaign to submit no more than 6,000.

At a campaign event before submitting the signatures, King suggested he could be an instrumental member of a “centrist coalition” of senators who work together to break Senate logjams on important issues.

“I think there’s an opportunity for a small group who can have a great impact on modern history,” King told a crowd of supporters at the State House.

King has refused to say whether he plans to caucus with Senate Democrats, Republicans or neither party if elected, and he said Tuesday that a senator without a party can exert influence in the 100-member body.

If Maine voters elect him, King said, “that in itself will send an important message to Washington.”

King will be one of at least three nonparty candidates in November’s Senate election. Brunswick resident Danny Dalton and Yarmouth Town Council chairman Steve Woods submitted their petitions and qualified for the ballot earlier this month, said Julie Flynn, the deputy secretary of state who heads the office’s Bureau of Corporations, Elections and Commissions.

Tea party activist Andrew Ian Dodge, who has also said he will run for the Senate seat as an independent, has made a Wednesday appointment with the secretary of state’s office, Flynn said.

Independent candidates have until Friday at 5 p.m. to submit at least 4,000 signatures.

Republicans and Democrats will make their picks for the Senate race on June 12.