It said ten people were killed and 15 wounded but gave no further details.
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Turkey is a popular destination for Germans, and Germany’s foreign ministry urged travelers in Istanbul “to avoid public gatherings (and) tourist attractions for now” after the attack.
Out of 15 injured, nine are reported to be German.
Turkish authorities have said a 28-year-old Syrian national carried out the attack in Istanbul’s historic Sultanahmet district, a main tourist hub.
Shortly after the blast, Germany had warned its nationals to avoid tourist sites in Istanbul, a city of 14 million that has been hit several times by deadly attacks.
“They attacked Sultanahmet to grab attention because this is what the world thinks of when it thinks of Turkey”, said Kursat Yilmaz, who has operated tours for 25 years from an office by the square.
The boring thud of the explosion was heard in districts of Istanbul several kilometres away, residents said.
Al Jazeera’s Emre Rende, reporting from Istanbul, said information was scarce immediately after the blast.
Turkey’s state-run news agency said Davutoglu held a telephone conversation with German chancellor Angela Merkel to express his condolences.
A Kurdish splinter group, the Freedom Falcons of Kurdistan (TAK), claimed a mortar attack on Istanbul’s second worldwide airport on December 23 which killed a female cleaner and damaged several planes.
Erdogan did not specify which group, specifically, his government thinks is responsible for Tuesday’s explosion, which happened between the Hagia Sofia and Blue Mosque tourist attractions in the cultural and historic heart of the city.
Police secure the area after an explosion in central Istanbul, Turkey January 12, 2016.
Police cordoned off the area to shocked passers-by and tourists and the nearby tram service has been halted.
President Recep Tayyip Erdogan initially said the attacker had Syrian roots.
“Investigations into the cause of the explosion, the type of explosion and perpetrator or perpetrators are underway”, it said in a statement quoted by the Dogan news agency.
“This incident showed one more time that we should be united against terror”, Erdogan said. The blast came after a slew of deadly attacks across Turkey in past months that has left Turkey’s largest city on edge.
Tuesday’s blast rattled Sultanahmet Square around 10:20 a.m. (3:20 a.m. ET) and brought a rush of ambulances and security forces to an area that would have been heavily guarded on any day.
Turkey has become a target for the Islamic State of Iraq and the Levant (ISIL), with two bombings previous year blamed on the armed group, in the town of Suruc near the Syrian border and in the capital Ankara.
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Two suicide bombs in October outside Ankara’s main train station as people gathered for a peace rally killed more than 100 people.
