“Our priority is the health of the hostages. Hence we appeal to the kidnappers to free the hostages unconditionally,” Gusenbauer said on Friday.
Speaking to reporters at a European Union summit in Brussels, Gusenbauer stressed that Austria was a peaceful country.
A statement posted on a website attributed to al-Qaeda gave Austrian authorities three days to comply, starting midnight on Thursday.
“The state of Austria is responsible for the lives of the two hostages in the event of the expiration of the time-period and not responding to our demands,” said the statement, which included six photographs purportedly showing the hostages Wolfgang Ebner and Andrea Kloiber.
The statement’s authenticity could not be independently verified although it was posted on a website linked to the group, according to an online monitoring agency, Site.
Vienna said this week that it was doing all it could to find the two and that an extensive search was under way.
Relatives reported the pair missing when they did not return from a vacation to Tunisia on March 1.
Austrian media identified Ebner as a 51-year-old tax consultant from the town of Hallein, and said 43-year-old Kloiber, a nurse, is his girlfriend.
Arabic daily Annahar had reported earlier that the hostages had been taken by their kidnappers to northern Mali.
The authorities began a search for the two tourists after Al Jazeera aired an audio tape, said to be from al-Qaeda’s North African branch, which linked the abduction to the violence in Gaza.
It said the man and woman were taken on February 22 and that they were in good health.
The tape also warned Western tourists to stay away from the Maghreb region in North Africa where Tunisia is.
“We tell Western tourists flocking to Tunisia for leisure at a time when our brethren are being slaughtered in Gaza by the Jews with the complicity of Western states … the apostate Tunisian state is not able, and will not be able, to protect you,” the voice on the tape warned.
The Tunisian government said it had carried out “intensive search operations” but there was no proof of the two tourists being in the country.
Meanwhile the US state department issued a warning to travellers to Tunisia in the wake of the kidnappings.
“Al-Qaeda Islamic Maghreb is designated as a terrorist organisation by the United States, and its presence in North Africa presents potential dangers to travellers,” a statement said.