BOSTON — Backers of an underground rail connection between Boston’s North Station and South Station have met at the Statehouse to help organize public support for the proposal.

The group is hoping to persuade Republican Gov. Charlie Baker to consider the rail link, which they say would provide for the possibility of uninterrupted Amtrak passenger service between Washington, D.C., and Maine.

Former Govs. Michael Dukakis, a Democrat, and William Weld, a Republican, have endorsed the plan.

Dukakis, speaking with reporters at the Statehouse on Monday, said the next step is “lots of advocacy, lots of debate, lots of discussion.”

Baker has expressed skepticism, saying “the devil is very much in the details.”

The supporters’ group includes Somerville Mayor Joseph Curtatone, Salem Mayor Kim Driscoll, Quincy Mayor Tom Koch, Fitchburg Mayor Lisa Wong and Newton Mayor Setti Warren.