The following video shows the damage sustained in the village of Castelluccio, near Norcia.
Firefighters pulled a dog alive from the rubble 35 hours after Italy's strongest natural disaster in decades hit the country's central parts on Sunday.
Italy's Civil Protection Department on Monday said more than 15,000 people have been housed by authorities due to tremors since the August 24 quake.
There were no deaths or serious injuries after Sunday morning's 6.6-magnitude tremor, largely because most fragile city centres had already been closed because of previous damage and many homes had been vacated. There have been no reports of human or animal deaths. Temperatures overnight reached near freezing, and officials have expressed concern for the many elderly residents of the mountain communities.
"We can not have tents for some months in the mountains, under the snow", Renzi wrote in a message.
You can see the cracked facades of both churches still standing in the footage above, but most of their structure has collapsed into rubble. "There are enough hotels for everyone".
Premier Matteo Renzi visited the town of Preci with his wife to survey the damage, meet some of the displaced people and participate in an open-air mass for All Saints' Day. Mayor Nicola Alemanno said tents that can house a couple of thousand people had been erected, while 500 have moved to hotels.
Two important churches in Norcia were destroyed by the shock: the 14th century Basilica of St Benedict, which was built on the traditional birthplace of St Benedict, founder of the Benedictine monastic order; and the 15th century Cathedra of St Mary Argentea.
"We will rebuild everything in a timely manner", he said, according to news agency ANSA.
Following the destruction of the basilica built atop the birthplace of their founder, the Benedictine monks said they hoped the image of the destroyed church may "serve to illustrate the power of this natural disaster and the urgency we monks feel to seek out those who need the Sacraments on this hard day for Italy".