Mohammed Nadeem, a local police official, said fighting escalated after clashes began when armed men opened fire on a Sunni mosque.
Abdul Ghafoor, a local Sunni leader, confirmed the police chief's reports saying that Shias had initiated the violence by opening fire at their mosque.
"They [Shia men] have killed dozens of our people," he said.
But Abid Hussain, a leader for Parachinar's Shia community, accused Sunni fighters from nearby towns of starting the violence by firing rockets at their homes and mosques.
"We are only defending ourselves," he said.
Hussain said that dozens from his community had been killed.
Officials in the semi-autonomous tribal region said at least 10 bodies were handed over to their relatives in the Alizai area of the town.
Witnesses said the fighters used heavy weapons including mortars and rocket launchers.
A curfew had been imposed in troubled parts of the town, but reports have suggested that fighting is still taking place.
Most of the ethnic Pashtun tribesmen in Kurram are Shia, although most Pashtuns are Sunni, and in April, about 40 people were killed in the region in an outbreak of sectarian violence.
Pakistan's Shias account for about 15 per cent of the country's 160 million people.