The New York attorney general’s office said Friday that it had tracked about $1 billion in wire transfers by the Sackler family, including through Swiss bank accounts, suggesting that the family tried to shield wealth as it faced a raft of litigation over its role in the opioid crisis.

Earlier this week, thousands of municipal governments and nearly two dozen states tentatively reached a settlement with the Sackler family and the company it owns, Purdue Pharma, maker of OxyContin. But the attorneys general of a majority of states, including New York and Massachusetts, are balking at the proposed deal, contending that the Sackler family has siphoned off company profits that should be used to pay for the billions of dollars in damage caused by opioids.

The wire transfers are part of a lawsuit against Purdue and individual Sacklers in New York. Letitia James, now the state’s attorney general, had issued subpoenas last month to 33 financial institutions and investment advisers with ties to the Sacklers in an effort to trace the full measure of the family’s wealth.

“While the Sacklers continue to lowball victims and skirt a responsible settlement, we refuse to allow the family to misuse the courts in an effort to shield their financial misconduct,” Ms. James said in a statement. “Records from one financial institution alone have shown approximately $1 billion in wire transfers between the Sacklers, entities they control, and different financial institutions, including those that have funneled funds into Swiss bank accounts,” she added.