The statement's authenticity could not be independently verified although it was posted on a website linked to the group, according to online monitoring agency, SITE.
The Austrian foreign ministry confirmed that it had received the ultimatum but there were no details on how many prisoners were being demanded.
Vienna said this week that it was doing all it could to find the two and that an extensive search was under way in an area the size of Austria.
Relatives reported the pair missing when they did not return from a vacation to Tunisia on March 1.
The two were last heard from on February 18 and failed to make a planned phone call to Ebner's son on February 25.
Austrian media identified Ebner as a 51-year-old tax consultant from the town of Hallein, and said 43-year-old Kloiber is his girlfriend.
Arabic daily Annahar had reported earlier that the Austrian man and woman hostage had been taken by their kidnappers to northern Mali.
Anis Rahmani, Annar's chief, said "Algeria's army had channelled the kidnappers towards Libya and Mali, where the possibility of negotiations with the Austrian authorities for an eventual release of the hostages is greater".
The authorities began a search for the two tourists after Al Jazeera's Arabic channel aired an audio tape, said to be from al-Qaeda's North African branch, which linked the abduction of the consultant and nurse 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.
It said the Austrians were last heard of crossing the Sahara desert in a direction that would have taken them out of Tunisia.
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," said the statement.