Six civilians and four officers were wounded.
A statement given by Frans Barung Mangera, another police rep offered assurances about the 8-year-old girl's chances of survival.
At least four children belonging to two of the three families behind the string of bombings in Surabaya and Sidoarjo, East Java, on Sunday and Monday, became orphans after their parents were killed in the explosions.
Police ordered the temporary closure of all churches in Surabaya on Sunday, and a large food festival in the city was cancelled.
Terrorist organisations such as Islamic State, al-Quaeda, the Taliban, and this latest group - the so called Jemaah Anshorut Daulah or JAD, want to spread fear, chaos, civil unrest and uncertainty in order to weaken political, social and civil power structures and draw new recruits to their evil cause.
Such groups, which are loyal to the Islamic State in Iraq and Syria, as well as returnees from ISIS territories in the Middle East, pose a growing new threat in Indonesia, said Mr Evan Laksmana, a senior researcher at the Jakarta-based Centre for Strategic and International Studies.
In all, 26 people - including 13 militants and their children - died since Sunday.
Corrected: 89% of non-OPEC 2018 supply growth from US - OPEC
With more than 1 200 people wounded by live fire, it was the deadliest day in Gaza since Hamas's last war with Israel in 2014. Consequently, the price of Brent and WTI rose from $76.80 to $77.99 and $70.50 to $70.91 respectively in the global market.
ISIS, from which the recent attackers reportedly took their cues, has always understood the power of using provocative violence, Barton said.
Democratic Party deputy secretary-general Rachland Nashidik said that while it was important to revise the Terrorism Law, the President should "pay attention to organizational reform and replace officials who have failed in carrying out their duties to protect the freedom and security of citizens".
Earlier on Tuesday, police searched the home of the family that bombed Surabaya's police headquarters and found unexploded bombs.
The archipelago nation of some 17,000 islands has long struggled with radical militancy, including the 2002 Bali bombings that killed 202 people - mostly foreign tourists - in the country's worst-ever terror attack. Its leaders were killed in police raids and hundreds of militants were arrested.
Tito said it was the first time that terrorists in Indonesia had taken along children in their suicide bombings.
Karnavian said the father drove a bomb-laden vehicle into the city's Pentecostal church. The church bombings were swiftly followed by other attacks, including one Monday that targeted a police station and was carried out in the company of the attackers' 7-year-old daughter.