A tentative national deal was agreed last week, but refinery operators are continuing to hold talks with local unions in an effort to end the biggest refinery strike in the United States for 35 years, CNBC reported.

On March 12 the United Steelworkers (USW) and lead industry negotiator Royal Dutch Shell plc shook hands on a tentative four-year contract.

The deal includes yearly wage increases as well as an agreement to maintain the current healthcare plan cost-sharing ratio. After safety concerns were raised by the USW, the new contract also includes an immediate review of staffing and workload assessments and addresses daily maintenance and repair work, the union said.

The agreement is designed to set industry-wide standards but it still needs to be approved at each site.

Among the facilities that look set to approve a new contract is the largest U.S. refinery, operated by Motiva Enterprises in Port Arthur, Texas. Three other plants were also said to be making progress.

Workers at these refineries could return to work as early as next week, but at other facilities contract talks have stalled as local union negotiators try to reach a deal on issues not covered by the national agreement. As a result, many plants will continue to rely on temporary workers to keep operating.

The work stoppage has affected refineries accounting for one-fifth of U.S. processing capacity.