ISIS has claimed responsibility for an attack that left four Christians dead in southwestern Pakistan on Easter Monday.

A press statement from the terror group on Tuesday said a 'covert unit' of militants 'managed to target a number of the combatant Christians'. It added the jihadists 'shot them with a pistol, which resulted in the killing of four of them, and all praise is due to Allah'.

The family were travelling in a rickshaw when the attackers opened fire, killing three of them plus the driver. One woman survived and was taken to hospital, police said. However her father and three cousins died.

'It appears to have been a targeted attack,' provincial police official Moazzam Jah Ansari told Reuters. 'It was an act of terrorism.'

ISIS has not provided any evidence of its involvement.

The attack comes a day after Pakistan's Christian community celebrated Easter on Sunday. Around two per cent of Pakistan's population are Christians.

Minority religious festivals are a security concern in the majority Sunni Muslim country where there have been a number of high casualty attacks on Christians and Shi'ite Muslims. In 2016 on Easter Sunday an explosion at the hospital in Quetta killed 72 people and a bombing in the eastern city of Lahore killed at least 69 people.

Monday's attack took place in Quetta city, the capital of Baluchistan province, which borders Iran as well as Afghanistan. The region is plagued by violence by Sunni Islamist sectarian groups linked to the Taliban, al Qaeda and Islamic State. It also has an indigenous ethnic Baloch insurgency fighting against central government.

In December, a week before Christmas, two suicide bombers stormed a packed Christian church in southwestern Pakistan, killing at least 10 people and wounding up to 56, in an attack claimed by Islamic State.

The family killed on Monday had come to visit relatives in Quetta's Shahzaman road area, where a large number of the city's Christian community lives.

Additional reporting by Reuters.