He also promised that people who have returned to Austria after travelling to Syria to join Isis, the terror group also known as Islamic State, would be under increased surveillance.
“We won't let terrorists destroy democracy," Faymann insisted in an interview on ORF television. He added that it would be “completely wrong” to start blaming refugees for the attacks carried out by Isis.
He said that random identity checks on people entering Austria would continue and become more frequent, and called for migrants to all be registered as they arrive at the EU's external borders.
On Monday evening Slovenia's Prime Minister asked Austria not to build a fence on its northern border with Slovenia, saying it was not in the countries' common interest.
Security measures 'not visible'
Whilst Austria's neighbours - including Italy, Hungary and Germany - remain on high alert in case of another terror attack the Austrian government has said there is no official terror alert and has not gone into any detail about its security measures.
The police presence around French institutions in Austria has been increased, as well as at the Hotel Imperial in Vienna where diplomatic talks have been held on how to end the war in Syria. There will also be greater security at an international soccer match between Switzerland and Austria on Tuesday.
However, the Kurier newspaper reports that no additional security measures are in evidence at Vienna airport and there is a distinct lack of armed police at the airport and at main train stations.
Austria's special forces police are reported to be on high alert and sources at the interior ministry said that Interior Minister Johanna Mikl-Leitner has offered her French counterpart a backup task force if needed.