Local legislators are forging ahead with their efforts to restore weekend commuter rail service to the South Shore.

Representative Josh Cutler of Duxbury updated the Board of Selectmen on this issue Monday night. He said that on April 29, the House approved an amendment to the budget that would require the Massachusetts Bay Transit Authority to examine and report on the feasibility of restoring weekend rail service to the Kingston/Plymouth and Greenbush lines.

The amendment orders the MBTA to look at the many issues involved in restoring weekend rail service, including the costs and the numbers of riders needed to make the train service feasible. It also seeks a comparison of costs and ridership on other commuter rail lines that run weekend trains.

If the amendment survives budget deliberations, it would require the MBTA to file its report by Nov. 30.

Before the service ended, trains to Boston ran more than six round-trips on a weekend.

The MBTA discounted weekend service on the Kingston/Plymouth and Greenbush lines as well as the Needham line in July 2012 as part of a cost-cutting plan to close a budget deficit.

Cutler and many other South Shore representatives are backing the weekend rail restoration and are meeting with the MBTA to get both answers and action.

“We’re continuing to push forward,” Cutler said.