ROME — Pope Francis has rejected the resignation of a French cardinal, the Vatican announced on Tuesday, despite the cardinal’s conviction this month for covering up decades-old allegations of sexual abuse by a priest in his diocese.

A French court found Cardinal Philippe Barbarin, archbishop of Lyon, guilty on March 7 of failing to report abuse to the authorities, and imposed a six-month suspended sentence.

Cardinal Barbarin, 68, promptly offered to resign, though he is appealing the verdict. He met with Pope Francis on Monday to personally hand in his resignation, but both the cardinal and a Vatican spokesman, Alessandro Gisotti, said on Tuesday that the pope had not accepted it.

Instead, they said, the cardinal, one of the highest-ranking and best-known Roman Catholic officials in France, will step aside for an unspecified length of time.