Wal-Mart said on Tuesday that it would pay at least $352 million, and possibly far more, to settle lawsuits across the country claiming that it forced employees to work off the clock. Several lawyers described it as the largest settlement ever for lawsuits over wage violations.

After years of being embarrassed by lawsuits over its wage practices, the company agreed to settle 63 cases pending in federal and state courts in 42 states.

The workers and their lawyers will receive at least $352 million, and the payments could reach $640 million, depending on how many claims affected workers submit.

Union critics of Wal-Mart, the world’s largest retailer, saw the settlement as proof of their view that the company achieves its low prices in part by cheating workers. But the company rejected that characterization, saying it had already corrected wage practices that it has long attributed to local managers acting without authority.