There has been a 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 could not understand.
"We have been carrying out an operation since July 12 ... We have caught 6,122 people in Istanbul, including 2,600 Afghans and around 1,000 Syrians," Soylu told TV station NTV on Wednesday.
"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 and denying the claims of deportation.
However, he said some Syrians were "voluntarily" choosing to go back to areas in Syria where fighting has abated.
Turkey is home to 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 first registered.
On July 18, the Interior Ministry's Directorate of Migration Management said in a statement that it was illegal for refugees with protection permits to stay in provinces other than the one in which they were registered.
The statement said that violations of the rule will be penalised, which might include the revocation of permits.
The current crackdown is aimed at those who live in Istanbul without a permit to stay in the city.
International and national media reports earlier this week said that hundreds of refugees with protection permits issued in other provinces were detained 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 Justice and Development (AK) Party in the Istanbul mayoral elections earlier this year, 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.