BOSTON (AP) — A judge has pledged to waive mounting fines against striking teachers in three Massachusetts communities for Friday if they agree to return to the classroom by Monday.

Classrooms remained shuttered in Beverly, Gloucester and Marblehead — three communities north of Boston — again on Friday, marking the end of the second full week that teachers have taken to the picket lines.

The strikes have kept thousands of students across the three communities at home and will force schools to hold classes during vacations and weekends to meet the required 180 days of classroom learning required by state law — a situation that any snow days could make worse.

An Essex County Superior Court judge also said that if there is no deal by 6 p.m. Sunday a third party will take over the talks between striking teachers and local officials.

Teacher strikes are illegal in Massachusetts.

Teachers in Beverly said Thursday that they have reduced their wage proposals, but accused town officials of dragging out the negotiations. Union representatives said they were willing to keep talks going around the clock if necessary.

“The inaction of the school committee is why schools are closed. We are really trying to bargain here. We all want to go back to school,” Andrea Sherman. co-president Beverly Teachers Association said Thursday evening.

Rachael Abell, president of the Beverly School Committee, pointed to the unions for the extended negotiations, saying they rejected an offer to add nearly $2 million for teacher and paraprofessional salaries.

“The union spent very little time reviewing and then essentially insisted on their initial demands, which are way beyond what is affordable to the city,” she said after Thursday’s negotiations.

The Beverly Teachers Association has said it is pushing for smaller class sizes in the 4,500-student district, 12 weeks of paid parental leave and a “living wage” for paraprofessionals or teachers assistants whose starting salary is $20,000.

In Gloucester, the union in the 2,800-student district has asked for at least eight weeks of fully paid parental leave. It also wants significant pay increases for paraprofessionals, safer conditions for students and more prep time for elementary school teachers.

On Nov. 12, judges imposed a fine of $50,000 on the unions in Beverly and Gloucester that they said would increase by $10,000 for every day the teachers remained on strike. The unions voted Nov. 7 to authorize a strike and schools have remained closed.

Gov. Maura Healey has said her focus is getting students back into the classroom.