Soylu had threatened last week "to devastate" Istanbul Mayor Ekrem Imamoglu, of the main opposition Republican People's Party (CHP), over his support for the ousted mayors of the cities of Diyarbakir, Van and Mardin.
But in a CNN Turk interview on Sunday, Soylu said: "For Istanbul and Ankara, for such thing to be in question (appointment of a trustee) is not possible."
The three mayors were removed over alleged terror links less than five months after they were elected, sparking sharp criticism from the opposition including Ankara's CHP mayor Mansur Yavas.
Imamoglu - whose election in June dealt President Tayyip Erdogan's AK Party (AKP) a shock defeat - has labeled the move illegal and undemocratic and called for it to be reversed. He visited two of the ousted mayors in Diyarbakir last month.
Imamoglu on Sunday dismissed Soylu's threat as "upsetting" politics.
"It shouldn't become a tradition in this country to blame someone without any judgment. It is against jurisdiction and law," Imamoglu said at a news conference to discuss what he called wasted public funds under previous AKP administrations.
"All of the 82 million people in Turkey are my citizens... What I did was in line with the law and for propagating the national sentiment to all around the country," he said of his visit to Diyarbakir.
His municipality has parked in an Istanbul lot hundreds of cars it says were rented by previous administrations and that represent wasted public funds. He said the cars would be returned and the money spent on public parks.