There has been concern in recent days over reports that hundreds of Syrian refugees have been sent back to Syria, after being forced to sign consent forms in Turkish that they do not understand.
Soylu denied the claims.
"We have been carrying out an operation since July 12... We have caught 6,122 people in Istanbul, including 2,600 Afghans," Interior Minister Suleyman Soylu told TV station NTV.
He said Syrians were part of the group, without giving numbers.
"When we catch Syrians who are not registered, we send them to refugee camps," he said, citing a camp in the Turkish border province of Hatay.
However, he said some Syrians were choosing to go back to their home country "voluntarily" to areas where fighting has abated.
Turkey has more than 3.5 million Syrian refugees -- the highest number in the world.
Most have "temporary protection" permits but these restrict them to the province in which they were registered. The current crackdown is aimed at those who live in Istanbul without a permit to stay in the city.
A coalition of Syrian NGOs said Monday that more than 600 Syrians -- mostly with protection permits issued in other provinces -- were arrested in Istanbul last week and deported back to Syria, rather than to their assigned provinces.
The crackdown is orchestrated by the Istanbul governor's office, which is controlled by the central government in Ankara.
It follows the defeat of President Recep Tayyip Erdogan's AKP party in the Istanbul party, with some arguing that the large presence of refugees in the city had hurt the ruling party's popularity.
The governor's office says there are 547,000 Syrians registered in the city.
A survey published this month by Kadir Has University in Istanbul showed growing hostility towards them, rising from 54.5 percent of respondents in 2017 to 67.7 percent in 2019.