"An inter-religious dialogue centre that remains silent when it is time to speak out clearly for human rights is not worthy of being called a dialogue centre. It is a silence centre," Werner Faymann told radio station Ö1.
"It cannot be possible that we have a centre in Austria with the title 'inter-religious dialogue' while at the same time someone who actually engages in this is in prison and fearing for his life," Faymann said.
Saudi blogger and co-founder of the Saudi Liberal Network, Raef Badawi, has been jailed since 2012. This month he received 50 lashes as the first of 20 weekly floggings that he was sentenced to in September concurrent with 10 years in prison for insulting Islam.
Several countries including the United States -- along with the UN human rights chief, rights groups and academics -- have sharply criticised the sentence. Badawi's second flogging session was postponed last week on medical grounds.
The King Abdullah Bin Abdulaziz International Centre for Interreligious and Intercultural Dialogue (KAICIID) was opened in Vienna with great pomp by UN chief Ban Ki-moon and senior figures from the world's main religions in 2012.
Having come under considerable public pressure of late, the KAICIID has said that it condemns all forms of violence, but has not spoken out specifically about Badawi. It says it does not want to get involved in the internal affairs of other countries.
Its Austrian deputy leader resigned on Monday, after coming under pressure for comments which played down Saudi Arabia's human rights record.
Other members of Faymann's government, notably Foreign Minister Sebastian Kurz, who is from a different party than the centre-left chancellor, have been less outspoken.
Faymann said that he has ordered a report into the inter-governmental organization (IGO) to be completed by March.
"I will wait for the report to see whether this centre... has achieved anything that could allow it to be called a dialogue centre. For me, as long as the centre stays silent, it does not perform this function," Faymann said.