Chief executives of a handful of pharmaceutical and drug distribution companies were negotiating Friday with government attorneys to see if they can reach a settlement ahead of the first federal trial over the U.S. opioid crisis.

The federal judge who is overseeing more than 2,000 opioid-related lawsuits summoned the top officials for the companies that are defendants in the case.

Jurors in U.S. District Court in Cleveland are to hear claims from two Ohio counties, Cuyahoga and Summit, with opening statements scheduled for Monday. Witnesses expected to be called during the opening days of testimony include two experts on addiction, an official with the Summit County Alcohol, Drug Addiction and Mental Health Service Board, a fire chief and Travis Bornstein, whose son Tyler fatally overdosed in 2014 at age 18.

Judge Dan Polster has said he wants the parties to strike a settlement in such a way that it would make a real difference in resolving the crisis, which has killed more than 400,000 Americans since 2000. He invited state attorneys general to participate in the negotiations even though their lawsuits against the industry were filed in state courts.

Four attorneys general were at Friday's meetings, according to a source with knowledge of the negotiations but who was not authorized to speak about them publicly.

With the first trial about to begin, there is still some chance of a grand bargain that could resolve all the lawsuits.

Several smaller settlements have already been reached. Four drugmakers, including Johnson & Johnson, settled with the two Ohio counties in deals that got them out of the first trial and bought more time for them to reach a larger settlement. OxyContin maker Purdue Pharma has a tentative settlement with many of the plaintiffs and is trying to finalize it through bankruptcy court in New York, where the deal could be reworked.

After those settlements and agreements to remove other companies from the first trial, just a half dozen companies remain as defendants: drugmaker Teva on behalf of two subsidiaries; the dominant distributors AmerisourceBergen, Cardinal Health and McKesson; the pharmacy chain Walgreens in its role as a distributor; and the smaller distributor Henry Schein.

Johnson & Johnson, Teva and the three big distributors have been working on a way to settle all the cases against them.