AUGUSTA — Maine Democrats and Republicans are advancing revamped congressional redistricting plans as they try to close the gap on widely differing proposals offered earlier this week.

The chairman of the state Reapportionment Commission, Michael Friedman, encouraged the two sides to come closer to an agreement when they presented their plans Monday. Friedman held out hope they could agree on a single plan before a public hearing next Tuesday, or at least find a middle ground.

A public hearing is scheduled for 9 a.m. Tuesday in the Appropriations Committee room at the State House in Augusta.

Democrats offered a plan today that shifts additional towns from the 1st to 2nd congressional districts. Republicans presented several options they say address the concerns of Democrats.

Federal courts have ordered congressional districts updated to reflect changes in the 2010 census. Lawmakers have to find a way to even out the population of the state’s two congressional districts, which amounts to adding about 4,000 people to the 2nd District. The Legislature has scheduled a Sept. 27 special session to consider a plan.