Talks resumed Tuesday in an effort to break the deadlock between Royal Dutch Shell and the United Steelworkers Union (USW) in a dispute that has triggered the biggest refinery strike in the United States for 35 years.

The union, which represents employees at more than 200 refineries, oil terminals, pipelines and petrochemical plants, called a strike at nine refineries on Sunday after negotiations over a new three-year labor contract broke down. Collectively, these sites account for 10 percent of the country's refining capacity.

Some 3,800 workers are participating in the strike, according to union spokeswoman Lynne Hancock.

The remaining USW-represented refineries and oil facilities are operating under a rolling 24-hour contract extension, the union said.

Data compiled by Bloomberg shows that the refineries involved in the strike can produce 1.82 million barrels of fuel a day. Most have not stopped production; the operators have contingency plans in place to keep the refineries going.

According to reports, USW rejected five offers made by Royal Dutch Shell on behalf of companies including Exxon Mobil and Chevron before initiating the strike.

The union wants employers to improve pay, working conditions and safety for refinery employees.

USW spokesman Gary Beevers said: "This work stoppage is about onerous overtime; unsafe staffing levels; dangerous conditions the industry continues to ignore; the daily occurrences of fires, emissions, leaks and explosions that threaten local communities without the industry doing much about it; the industry's refusal to make opportunities for workers in the trade crafts; the flagrant contracting out that impacts health and safety on the job; and the erosion of our workplace, where qualified and experienced union workers are replaced by contractors when they leave or retire."