AUGUSTA — A proposal to let Maine voters rather than the Legislature elect three prominent state officials was rejected Monday by the state Senate.

The bill was turned back by an 18-16 vote against after some lawmakers argued it wasn’t needed.

The measure seeks a constitutional amendment providing for the direct popular election beginning in 2014 of the secretary of state and treasurer every two years, and for attorney general every four years. The House and Senate would have to approve the bill by two-thirds votes in order to send it to voters for their approval.

The secretary of state’s office conducts state elections, administers motor vehicle registration, licensing and testing, oversees the state archives and keeps records relating to more than 80,000 businesses and nonprofit corporations. The treasurer’s office manages the state’s cash and debt and represents Maine in the sale of state bonds. The attorney general represents the state in legal civil disputes and prosecutes the more severe crimes.

Despite the prominence of those jobs, Maine remains one of only a handful of states that does not allow voters to directly elect their occupants, said the bill’s sponsor, Sen. Andre Cushing, R-Hampden. Direct elections would also draw candidates who are better qualified for the positions and make them more answerable to the public, supporters said.

But opponents said the present system exposes candidates the sufficient vetting, and described the bill as a solution in search of a problem.

“We don’t have a problem that needs fixing,” said Sen. Emily Ann Cain, D-Orono.

Cain said Maine already has robust slates of statewide elections and doesn’t need more campaigns and pre-election spending, adding that the bill “will only bring us closer to states we mock.”

The bill faced a vote in the House.