ROME—Pope Francis declined to accept the resignation of a French cardinal convicted of covering up sexual abuse, the Vatican said on Tuesday, a decision that drew fire from victims and their advocates in France and abroad.

Cardinal Philippe Barbarin of Lyon had offered to step down in a private meeting with the pontiff on Monday.

The cardinal issued a statement similar to the Vatican’s on Tuesday, adding that the pope had cited the “presumption of [the cardinal’s] innocence” in declining to accept his resignation.

This month, Cardinal Barbarin became the highest-ranking Catholic Church official ever to be convicted of covering up sexual abuse, in the latest chapter of the church’s long-running abuse scandal.

The Vatican said the pope had left the cardinal “free to make the best decision” for the Lyon archdiocese, which has about 1.2 million Catholics. It said the cardinal had decided to take leave of his duties “for a period of time,” and entrust the leadership of the archdiocese to his vicar general, the Rev. Yves Baumgarten.