Opioid Distributors Are Asked to Boost Offer to End Litigation

States are pushing drug distributors McKesson Corp., Cardinal Health Inc. and AmerisourceBergen Corp. to add $2.3 billion to their $19.2 billion proposal to resolve government lawsuits over the U.S. opioid epidemic.

A majority of the state attorneys general are seeking the added funds to bring the total settlement package, including $4 billion from drugmaker Johnson & Johnson, to about $25.5 billion, according to people familiar with the talks who asked not to be identified because they aren’t authorized to speak publicly.

It’s unclear if the three largest U.S. drug distributors are considering the request for a bigger payout, ...