Six suspects were in court for questioning by Turkish prosecutors over the deadly attack, the state-run Anatolia news agency reported.
The nationalities of the foreigners were not immediately available.
A female suicide bomber blew herself up last Tuesday in the Sultanahmet district of Istanbul, the location of most of the biggest historic tourist attractions in the megacity.
A policeman was killed and another injured in the attack.
Outlawed far-left Turkish militant group DHKP-C initially claimed responsibility but then retracted, saying the first statement was an error.
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Turkish Interior Minister Efkan Ala then announced Thursday that the identity of the bomber had been determined, but declined to give details.
Turkish media said the bomber had been named as Russian citizen Diana Ramazova from the Russian region of Dagestan.
Security has been high in Turkey over the past few months amid fears of attacks by Kurdish militants and jihadists controlling parts of Iraq and Syria up to the Turkish border.