Home Minister Sarfraz Bugti said one terrorist was killed at the gate while the other blew himself inside the church premises causing the casualties but prevented from reaching the prayer hall.
A local official said initial reports were that two suicide bombers stormed the church, one of whom was shot dead at the entrance of the church.
"We were in services when we heard a big bang", he said.
Pakistani officials denied that IS had an organised presence in the country, however, even though the terrorist group has claimed responsibility for several other attacks in Baluchistan in recent years.
Two women were among the dead, and 10 women and seven children were among the injured, hospital officials said.
"Suddenly a huge explosion occurred outside the hall that broke window panes", he told the newspaper.
A group funeral was held on Monday for the victims in the deadly suicide bombing at the church in Pakistan
The attack was followed by a blast, claiming the lives of at least five people and injuring 16 more, according to Quetta Deputy Commissioner Farukh Atiq, as quoted by the Tribune media outlet. The deadliest example was in September 2013, when twin suicide bomb blasts killed 85 people in a Peshawar church.
Sunday's incident was the first attack on a church claimed by an ISIS affiliate in Pakistan. About 60 people were also injured.
Pakistan's Christian minority is frequently the target of extermist attacks, and the government has provided the communities' churches with armed guards.
Bajwa also praised the "commendable" actions of law enforcement agencies and emergency services after the attack. There were 400 worshipers in the premises at the time of attack.
Meanwhile, Minister for Interior Ahsan Iqbal strongly condemned the terrorist attack, terming the incident tragic and an act of cowardliness.
He said Islam was a religion of peace and harmony and it taught its followers to respect worship places of all religions, adding that protecting religious freedom of the minorities was duty of the whole nation. "They are fighting against terrorists and our war will continue till complete elimination of the terrorists", he highlighted.