The mothers of the girls reported the priest, who has led the local church in the town of 4,200 people for several years, last week, Il Gazzetino reported.
Rumours of the abuse had been circulating in the town for some time before it was officially reported, the newspaper said.
The case comes weeks after the United Nations told the Vatican that is must remove all child sexual abusers from their posts and turn them over to the police.
For more than a decade, the Catholic Church has been rocked by a cascade of scandals around the world, with victims describing the trauma of abuse at the hands of people charged with their care.
The Vatican says it continues to receive around 600 claims against abusive priests every year, many dating back to the 1960s, 1970s and 1980s.
In February, a priest in Sicily was sentenced to a year in jail for paying children for sexual acts.
In another incident in December, a priest was given a two-and-a-half year sentence by a court in the north-eastern city of Pesaro for having sex with a 13-year-old girl.
Former Pope Benedict XVI apologized in 2010 for the "sinful and criminal" acts committed by members of the clergy, saying he was "truly sorry" and went on to defrock 400 offenders between 2011 and 2012.
His successor Pope Francis has said Catholics should feel "shame" for abuse and has presided over the creation of a commission to investigate sex crimes, enforce prevention and care for victims – though it has yet to begin work.
While several bishops have stepped down over scandals in their dioceses, victims and support groups demand someone be held legally accountable.