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WASHINGTON — The Biden administration on Tuesday formally began allowing Americans who had ordered free coronavirus tests this winter to request a second round of four tests per household, through the same U.S. Postal Service program that President Biden unveiled in January.

The move, which Mr. Biden had promised last week during his State of the Union address, followed a crush of interest in the program when it debuted in January. At the time, case rates had skyrocketed because of the Omicron variant and tens of millions of households scrambled to obtain the free tests.