Teamsters Local 25 and Republic Services walked away from the bargaining table on Tuesday, having made “little progress” on a deal to end the work stoppage.

State leaders urge Republic Services to finalize contract with striking Teamsters as uncollected garbage piles up in Massachusetts communities and other states across the country.

Some local union workers at Republic Services were honoring a strike in Boston by not crossing the picket line.

With his trash can in tow, rigged to a wagon on the back of his motorized wheelchair, Adam Elsbernd said he traveled nearly two miles to toss his trash at 2 a.m. to beat the daytime heat.

The fight between striking Massachusetts sanitation workers and the waste-management giant that employs them has entered a third week with no apparent signs either side is closer to making a deal. Local officials from impacted communities were joined earlier this week by Secretary of the Commonwealth Bill Galvin and members of the Boston City Council in calling for Republic Services to negotiate an end to the work stoppage which began on July 1.

Negotiations between Republic Services and Teamsters broke down late last week. Talks are set to resume Tuesday, but the impacts of the trash strike are growing more pronounced.

Boston officials are calling on Republic Services to return to the table and settle with trash workers, saying that the ongoing strike is a public health emergency.

Workers have walked off the job in parts of Los Angeles, Orange and San Diego counties, as well as the Bay Area.