Greater Boston communities at the center of the ongoing sanitation worker strike are taking Republic Services to court, seeking immediate relief as trash piles mount, attracting rats and giving off a sickening stench.

Gov. Maura Healey is backing the six cities and towns that have filed a complaint in Essex County Superior Court, calling for the waste management giant to resolve its dispute with striking members of Teamsters Local 25.

The two sides are slated to return to the negotiating table on Friday after failing to reach a deal in the last session on Tuesday. The company claims that Teamsters “changed their minds” about the scheduled end-of-week discussions after initially refusing to take its meeting offer.

Beverly, Malden, Gloucester, Peabody, Danvers and Canton are all behind the complaint seeking a preliminary injunction from the court that would require Republic Services to immediately collect all trash and recycling within the cities and towns and stop activities that are causing “nuisance conditions.”

Health directors from each of the six municipalities signed onto the complaint, highlighting how residents and businesses are dealing with rats in areas of piled-up trash, strong odors and overflowing dumpsters.

“The accumulation of trash and recycling throughout the municipalities has resulted in nuisances and sources of filth and causes of sicknesses,” the complaint states, “which may be injurious to the public health.

“Issuing a preliminary injunction serves the public interest,” it adds, “because it is necessary to prevent these conditions that have directly resulted from the defendant’s failure to provide full and regular weekly trash collection within the municipalities from further harming the public.”

The complaint, filed on Thursday, comes after leaders from the affected towns and cities wrote a letter to Republic Services last Friday. They demanded that the company “provide accurate and updated timelines and service expectations” and “expand driver resources and logistical support to guarantee the daily completion of all trash and recycling routes.”

Beverly Mayor Mike Cahill is following through on a threat to press fines against the company, a punishment outlined in last week’s letter.

In a memo to residents on Wednesday, the North Shore mayor said Republic Services has been notified that the city intends to “assess liquidated damages for trash and recycling not picked up and/or delayed in pickup and will withhold these amounts from our next scheduled payment.”

In response to a Herald inquiry, Republic Services called the court complaint “disappointing that these six communities have taken this route as we continue to work with our municipal partners to address their needs.”

“For example, (on Wednesday),” it added, “the City of Beverley stated on its website that ‘we continue to work closely with [Republic’s] current drivers, collectors, and supervisors, and Republic was able today to pick up most of the past week’s backlog of trash by the end of the day.’  A lawsuit merely distracts from the task at hand.

A hearing on the request for the preliminary injunction is scheduled for Monday afternoon at Essex County Superior Court in Salem, according to the docket.

Republic Services has filed a lawsuit of its own, asking a federal judge for a restraining order that would prevent Teamsters from engaging in alleged criminal negotiating tactics.

Following similar calls from other state leaders, Gov. Healey made her plea to Republic Services on Thursday for the company to reach a deal to end the strike.

“It has now been three weeks of no trash pickup in several Massachusetts communities,” the governor said in a statement, “and this has gone beyond a headache for residents, businesses and municipalities – it is a public health concern and it’s expensive for everyone.”

With sanitation workers on the picket line, communities are trying to overcome the burden and take piles of trash and recycling off their streets.

Danvers held a recycling drop-off event at its high school on Tuesday, drawing an “overwhelming response” that caused it to shut down early. Canton Little League is picking up trash and bringing it to the dump for a $20 donation.

It has gotten so dire in Peabody that the City Council has requested one of the wealthiest men in the world to step in for relief, Bill Gates. The Microsoft founder is the principal of Cascase Investment, LLC, a major shareholder of Republic Services.

“We respectfully urge you to use your influence,” the council wrote in a letter it sent to Gates earlier this week, “to take immediate and constructive action.”