AUGUSTA, Maine — Complaints about long lines and crowded rooms at Democratic and Republican caucuses last weekend have spurred legislative leaders to propose replacing Maine’s caucuses with state-run presidential primaries.

Senate minority leader Justin Alfond on Monday said he plans to submit legislation that would allow voters to select party nominees for president in a statewide election rather than at the party gatherings that traditionally have been used in Maine.

Alfond, a Democrat from Portland, noted that long lines at the Portland caucus on Sunday caused some people to wait more than four hours to vote. Some gave up and went home.

‘‘No one should be denied the right to vote,’’ Alfond said. ‘‘We need to do something better.’’

It would cost about $75,000 for the state to run a primary election, and each city and town would have to staff the local polls. Portland, for example, would have to spend about $50,000 to staff a primary election, according to the city.

While Democrats on Sunday held caucuses in 400 locations, Republicans on Saturday held them at 22 locations, and some rural counties had only one caucus for each county.

Senate president Michael Thibodeau, a Republican, said he heard complaints about the distance people had to travel to reach caucus locations and the crowds they encountered when they got there.

Thibodeau speculates most people would consider the additional cost of a primary a good investment if it allowed more people to vote.

House minority leader Ken Fredette, a Republican, said he is willing to cosponsor Alfond’s bill so lawmakers could discuss how to increase voter participation. House majority leader Jeff McCabe, a Democrat, also said he supports moving to a primary system.

Maine has traditionally used party-run caucuses to choose delegates for national political conventions. Maine switched to primaries for the 1996 and 2000 election, and then went back to the caucus system.

At the Democratic caucuses, people indicated support for a candidate by raising hands or breaking up into groups. Republicans at their caucuses voted by secret ballot.

Democratic Party chairman Phil Bartlett said caucuses help the party identify leaders at the local level. But he said the party is open to talking about moving to a primary system.

Governor Paul LePage also supports a primary system, said Maine Republican Party chairman Rick Bennett, who for years has advocated for switching to a primary election.

But Bennett said switching to primaries would require agreements with the national political parties, and it would be a challenge to schedule a primary election early enough so the results are relevant.

There will not be another presidential election until 2020, so there is no need for the state Legislature to take up the issue now, he said.