WASHINGTON—The number of U.S. workers filing for unemployment benefits weekly during the coronavirus pandemic has remained in record territory, but in recent weeks has dropped to about half the peak of 6.9 million touched in late March.

Weekly jobless claims—though still numbering in the millions, well above the prior weekly record of 695,000, set in 1982—suggest the wave of unemployment caused by the pandemic could crest as soon as this month. Still, the layoffs that already occurred are likely to cause the unemployment rate,…

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