"Freedom of the press is inviolable and a substantial pillar of a democratic society," Kickl said in a statement.
"A trustful relationship with the media is important to me, particularly in view of the sensitive material that our department handles. Any restriction of press freedom is completely unthinkable," the statement said.
Kickl's response came after the dailies Der Standard and Kurier published an email from his ministry which appeared to instruct the press departments of regional police forces to "limit communication with these media to the minimum
The email -- which the ministry had already confirmed earlier as authentic -- explicitly named Der Standard and Kurier. It also named the Falter weekly, which has carried out several investigations about the inner workings of the interior ministry in recent months.
The email also suggested that police highlight the nationality and immigration status of suspects in public statements about criminal cases.
The Kurier wrote in an editorial: "Our democracy should not die in darkness because a minister feels too weak to withstand criticism and is clearly unsuitable for this sensitive position."
Opposition parties were also up in arms, with members of the Social Democrats (SPÖ) calling for Kickl's resignation.
The interior ministry defended the contents of the leaked mail, but insisted that it did not originate from Kickl himself, but from his press spokesman, Christoph Pölzl.
Pölzl was quoted in Kickl's statement as saying that the wording of the email had been "a mistake", and insisted that the proposals had not in any way been intended as an order.
Austrian Chancellor Sebastian Kurz, currently attending the sidelines of the UN General Assembly in New York, had also said that attempt to "limit press freedom is unacceptable".
"Shutting out or boycotting specific media shouldn't happen in Austria," Austrian media reported Kurz as saying.
Kickl's far-right Freedom Party (FPÖ) shares power with Kurz's centre-right People's Party (OeVP) in a coalition that has been in power since December.
Kickl has been dogged by a scandal over government raids on Austria's BVT domestic intelligence agency in February.