NARRAGANSETT — The new Town Council won’t name a president until Monday night, but the early favorite appears to be someone who has lots of experience.

That would be T. Brian Handrigan, reelected on Nov. 7 to his sixth council term.

The 70-year-old Democrat said yesterday that the appointment is up to all five council members but he made no secret of his interest, and the other two Democrats on the new council said they will probably support him.

“I sat with him for two terms while he was president,” said George F. Lenihan Jr., who is returning to the council after a four-year absence. “He ran a good meeting. There was decorum, things were run professionally, he knows all the rules.”

James P. Durkin, returning for his third term, said that if he became president himself, Handrigan would be “correcting me all the time.” His solution?

“I think that I will vote for Brian,” he said.

The tone from the board’s Republicans was cautious but conciliatory.

Krista J. Garrett, who collected the highest vote total in winning her second term, said she is interested in the position given the support she received from voters and would like to see the matter discussed Monday. She also said she understands that the board’s three Democrats might look to Handrigan, given his experience.

“I believe in Brian’s seniority, I believe in Brian’s wisdom; I’m not opposed to that, but I believe that there’s a second seat available,” she said, referring to the position of president pro tempore. “If there’s a majority, I think that maybe the highest vote getter could get the second seat.”

Republican Christopher Wilkens, just elected to his first term, also wondered if Garrett should be considered for the president’s position but he said he is willing to vote for Handrigan if that’s what the majority wants.

“There’s no doubt about it. He would be an excellent president,” Wilkens said.

Handrigan, owner of Champlin’s Fish Market, served as president from 1996 to 2004, when Anne-Marie Silveira – who did not seek reelection this year – became president.

The president has an important role, serving as a mix of spokesman and communication conduit in addition to running the meetings.

Handrigan took issue with the notion that the highest vote getter usually becomes council president.

“That is not how it has worked in Narragansett,” he said, noting that he was not the top vote getter in any of the four terms he served as president. He also noted that Silveira was the highest vote getter in both of her terms yet served as president for only one.

“It’s not a popularity contest,” he said. “It’s basically who the council feels can handle the job best.”

Handrigan said the vote on who will be president will be the first order of business Monday night after the pledge of allegiance.