Saturday in the Gojra tehsil in Toba Tek Singh district of the province over the alleged desecration of the Holy Quran by one of the groups.
Fierce clashes broke out when a mob marched towards a village of the rival community to settle scores after the news spread.
The authorities on Sunday booked nearly 800 people for rioting and killing people, Geo TV said.
Meanwhile, on the orders of President Zardari a heavy contingent of police was immediately dispatched to the troubled area to bring the situation under control. The police had to open fire to stop the rampaging mobs, the Nation newspaper reported on its website.
Officials said 40 houses and a church were torched by one of the rival groups.
Tension has been running high between the Muslims and Christians in the area over the alleged desecration of the Holy Quran.
Television footage showed burning of houses, streets strewn with blackened furniture and people firing at one another from their rooftops.
Federal Minister for Minorities Shahbaz Bhatti alleged a mob "misled by extremists" attacked a Christian neighbourhood and torched dozens of houses.
"We have received six bodies with burn injuries - four women, a man and a child," Abdul Hamid, an official of the health ministry, said.
Zardari has directed the minority affairs minister to remain in Gojra until the situation becomes normal and to take steps for the security of people.
Punjab Law Minister Rana Sanaullah condemned the attack and said an inquiry has been ordered.
He said a preliminary investigation showed there was no desecration of the Holy Quran. "It was just a rumour which was exploited by anti-state elements to create chaos."
"I request both the Muslim and the Christian communities to show restraint," he said.
The government will take strict action against the rioters and police who failed to stop the violence, Sanaullah added.
Meanwhile, the families of the victims staged a protest against the killings by laying the bodies of their loved ones on the railway tracks.
The families demanded immediate arrests of those responsible for the violence.
Punjab Chief Minister Shahbaz Sharif has announced a compensation of Rs.500,000 for the families of the each of those killed in the violence.