WASHINGTON—The number of Americans who applied for first-time unemployment checks fell sharply last week to one of the lowest levels in four decades, bolstering the Federal Reserve’s view that the labor market is tightening.

Initial jobless claims, a measure of how many workers were laid off, declined 28,000 to a seasonally adjusted 235,000 in the week ended Dec. 31, the Labor Department said Thursday. That was the lowest level since mid-November and the second lowest since late 1973.

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