The magnitude-6.2 quake struck at 03:36 (01:36 GMT), 100km (65 miles) north-east of Rome, not far from Perugia.
Eighty-six of the dead were in the historic town of Amatrice, where the mayor said three-quarters of the town was destroyed, and in nearby Accumoli.
Many people are still believed to be buried under rubble.
Rescue teams are using heavy lifting equipment and their bare hands as they continue to search for survivors after nightfall.
There were cheers in the village of Pescara del Tronto when an eight-year-old girl was pulled alive from the rubble after being trapped for 17 hours.
“This is not a final toll,” Mr Renzi warned as he gave the latest figures on a visit to the area.
He had earlier paid tribute to the volunteers and civil defence officials who had rushed to the scene in the middle of the night and used their bare hands to dig for survivors.
He promised “no family, no city, no hamlet will be left behind”.
The tremor was felt across Italy, from Bologna in the north to Naples in the south. There have been dozens of aftershocks.
Hardest hit were the small towns and villages in the mountainous area where the regions of Umbria, Lazio and Le Marche meet.
As well as the 86 dead in two towns of Amatrice and Accumoli, there are 34 people known to have been killed in Le Marche province, including in the neighbouring villages of Arquata del Tronto and Pescara del Tronto.
Health minister Beatrice Lorenzin said there were many children among the dead
In Amatrice the missing include three nuns and four guests at their convent
In Accumoli the dead include a mother, father and their two young sons; rescuers had heard the screams of the mother and one of the children and had frantically tried to reach them in time, Italian media reported
Mayor Stefano Petrucci told Ansa that not a house in the town was fit for habitation, and they would have to set up tents to house everyone
Almost all houses in Pescara del Tronto have collapsed, the local mayor said
In Arquata, a grandmother saved her two grandchildren, aged four and seven, by pulling them under a bed with her.
Italy’s National Institute of Geophysics and Volcanology said it had recorded more than 200 aftershocks by 15:00 (13:00 GMT) on Wednesday.
The country is no stranger to earthquakes: in 2009 a tremor killed more than 300 people in L’Aquila and in May 2012 two tremors nine days apart killed more than 20 people in the northern Emilia Romagna region.
Rescue teams from around the country have been sent to the affected region.
The area is mountainous and access is difficult. Tent camps are being set up for those who need shelter, while others will be accommodated in buildings such as gymnasiums.
Many of the people affected were on holiday in the region.
The national blood donation service has appealed for donors to come forward.