A US Catholic bishop has resigned after he failed to alert authorities after child abuse images were found on a priest’s computer three years ago.

Robert W Finn, 62, of Kansas City was the only Catholic bishop to be convicted for not reporting suspicion of child abuse.

Groups representing victims of abuse by clerics had been urging Pope France to dismiss him.

Finn was the subject of a Vatican investigation that started last September into his leadership of the diocese of Kansas City-St Joseph, Missouri.

A Vatican statement said Pope Francis had accepted Finn's resignation.

A court in Kansas City convicted Finn in 2012 of failing to report suspected child abuse after the material was found on a computer of former priest of his diocese, Shawn Ratigan.

The bishop sent Ratigan to a therapist, moved him to a new job and ordered him to stay away from children.

The court sentenced Ratigan to 50 years in prison and Finn to two years of probation.             

An online petition asking the pope to remove Finn from the job has been signed by more than half a million people.             

Victims of abuse have been urging the Vatican to make bishops suspected of covering up abuse to be held accountable even if they did not commit the abuse themselves.