Updated

Australia will not give up its quest to prosecute an Australian Islamic State group suspect despite a Turkish court rejecting an extradition application, the Australian prime minister said on Friday.

Prime Minister Malcolm Turnbull said he was disappointed that the Criminal Court in the southern city of Kilis on Thursday rejected Australia's request to extradite Australian citizen Neil Prakash.

"We'll be working closely with the Turkish authorities to see how we can ensure that he is brought back to face justice in Australian courts.," Turnbull told reporters.

"He remains in custody in Turkey and we will do everything we can to that ensure Neil Prakash is brought to account for his crimes," Turnbull added.

Turnbull described the 27-year-old alleged militant recruiter as a threat to Australia and the Asia-Pacific region.

"Our goal is to ensure that Neil Prakash is not ever able to practice his evil trade of terrorism ever again," Turnbull said.

Turkish lawyer Mehmet Alper Unver said prosecutors, who argued for Prakash's extradition, had the right to appeal the verdict. Prakash could be freed from Turkish custody if the court ascertains that he is not under investigation for other crimes, Unver said.

Turnbull said Prakash also faced charges under Turkish law.

"The Turkish government is equally determined to deal with him," Turnbull said. "We will be working with them. Our job is to keep Australians safe and we are determined to keep Neil Prakash behind bars."

Prakash has been in Turkish custody near the border with Syria since 2016, after he attempted to enter Turkey with false documents.

The former rapper from Melbourne had featured in IS videos, has been linked to several attack plans in Australia and has urged lone wolf attacks against the United States.

He faces a potential life sentence if convicted in Australia of terrorism offenses.