The quake hit the same central regions that have been rocked by repeated tremors over the past two months.
Although it was bigger than an Aug. 24 earthquake that killed almost 300 people, no-one died on Sunday, but there was huge damage.
Weakened by repeated powerful jolts in recent weeks, many of Norcia's churches, monasteries and chapels, were wrecked.
The historic Basilica of St. Benedict, which stood on the main square of Norcia and was supposedly built over the birthplace of Benedict, the patron saint of Europe, and his sister St. Scolastica, was among those badly damaged by the tremors.
Italy's Civil Protection unit, which coordinates disaster relief, said numerous houses were destroyed on Sunday in the regions of Umbria and Marche, but either they were deserted at the time or most of the residents managed to escape in time.
Local authorities said towns and villages, including Amatrice and Pescara del Tronto, already battered by August's 6.2 quake had suffered further significant damage.
Experts said Sunday's quake was the strongest here since a 6.9 quake in Italy's south in 1980 that killed 2,735 people.
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