Ankara has said that yesterday's attack was carried out by a 28-year-old Syrian who belonged to the Islamic State (IS) group and had recently entered Turkey from Syria.
One person was arrested yesterday in connection with the bloodshed, Interior Minister Efkan Ala said today, without explaining the suspect's role in the strike.
Turkish security forces over the last two days rounded up 68 suspected IS members across the country, state media said, but it was not clear if any of them were directly connected to the Istanbul bombing.
The foreign ministry in Berlin said Wednesday all 10 of those killed in the attack were German. But de Maiziere said there was "no indication" the attack specifically targeted Germans, saying there was no need to cancel travel plans.
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"It was an attack against humanity," he said. "I see no reason to refrain from trips to Turkey."
But the German foreign ministry has advised its nationals to keep away from large groups in public places and tourist attractions in Istanbul.
Turkey has been hit by a string of deadly attacks blamed on jihadists over the last year, including a double suicide bombing in October in Ankara that killed more than 100 people.
But yesterday's bombing was the first time in recent memory tourists had been targeted in the heart of Istanbul.
The bomber, identified as Nabil Fadli, detonated his charge in Sultanahmet Square, home to Turkey's most visited historic sites including the Ottoman-era Blue Mosque and Hagia Sophia church.
The explosion went off by the Obelisk of Theodosius, a monument from ancient Egypt, one of the city's most iconic landmarks.
He was then fingerprinted by the Turkish migration service, explaining why the authorities were able to identify the bomber so rapidly after the attack.
The Hurriyet daily said Turkey's spy agency had twice issued warnings over the risk of a suicide attack in Istanbul.
Police today removed a cordon preventing access to the area of the attack, which was quickly thronged by media and some tourists, an AFP correspondent said.