During a Thursday meeting with Saudi Foreign Minister Adel al-Jubeir in Riyadh, Kurz said that he had also urged Saudi Arabia to create more opportunities for the relocation of the Syrian refugees in the Middle East, saying the kingdom has not done enough to that effect.
Before his trip to Riyadh, Kurz said that Austria is critical of the kingdom's violations of women's rights and that Saudi Arabia should provide a clear answer over the propagation of extremist ideologies abroad.
Meanwhile, the case of Saudi blogger Raif Badawi, whose flogging sentence created worldwide outrage, is still before the courts, al-Jubeir said on Thursday.
"The legal process is still ongoing and it's up to the courts to decide what happens in this case," Jubeir said at a press conference with Kurz.
Jubeir did not elaborate on what legal stage the case has reached, after Badawi's wife in June said Saudi Arabia's highest court had upheld a sentence of ten years' jail and 1,000 lashes against him.
Badawi, 31, received the first 50 lashes in January but there have been no more, following criticism from the European Union, United States, Sweden, Canada, the United Nations and others.
Jubeir said the Saudi judicial system, which is based on Islamic sharia law, is independent. "The Kingdom of Saudi Arabia respects the legal systems of every country and we expect other countries to respect our legal system," he said.
The European Parliament last month awarded Badawi its Sakharov human rights prize.
Announcing the award, parliament chief Martin Schulz called on King Salman to immediately release Badawi, denouncing his sentence as "brutal torture".
Badawi co-founded the Saudi Liberal Network Internet discussion group. He was detained in 2012 on cyber crime charges and later sentenced for insulting Islam.