"We recognize Mrs Bandion-Ortner’s step as one which will contribute to the stabilization of the current debate around the centre. We wish her all the best for the future," the centre's spokesman Peter Kaiser said in a press release.
Bandion-Ortner came under fire last year for comments that appeared to play down Saudi Arabia's human rights record.
On Saturday Austria’s Chancellor Werner Faymann called for the closure of the King Abdullah bin Abdulaziz International Centre for Interreligious and Intercultural Dialogue (KAICIID), which was opened in 2012.
Saudi Arabia bought the baroque palace that houses the centre, and covered its budget for the first three years.
"This centre does not fulfil at all the mandate of dialogue and is silent about basic issues of human rights. We will not tolerate this. It is clear to me from today's perspective that we should get out," Faymann told Der Standard newspaper.
Spain, Austria, and the Vatican are the political sponsors of the centre.
But senior politicians in Austria have asked how Saudi Arabia can have a dialogue centre in Vienna and also persecute free speech activists in their own country. The centre has faced increased criticism after the recent first round of punishment of Saudi blogger and activist Raif Badawi.
Last week 30-year-old Badawi received the first 50 lashes of a total of one thousand to which he was sentenced for having equated the different religions in an article he posted. He is also sentenced to 10 years in prison.
The Austrian section of Amnesty International organized a massive protest outside the Saudi Arabian embassy in Vienna on Friday.
Foreign Minister Sebastian Kurz of the conservative People's Party has called for restraint while he draws up a report by mid-year on whether KAICIID is fulfilling its mission.
Last November, senior Muslim, Christian and Jewish leaders condemned violence by jihadi militants such as Islamic State at a KAICIID conference.