"Let Austria, Tunisia and Algeria be responsible for the lives of the kidnapped."
Peter Launsky-Tieffenthal, Austria's foreign ministry spokesman, said before an earlier deadline expired on Sunday: "There are numerous ongoing contacts and we conclude from those contacts that more time is available to pursue comprehensive efforts leading to the release of Ms Kloiber and Mr Ebner."
Austrian officials have indicated that Austria will not be able to comply with the group's political demands since they concern the release of prisoners in Tunisia and Algeria beyond their jurisdiction.
Among the prisoners the group wanted released were former soldier Amar Saifi, known as El Para, or the The Paratrooper, a leading figure in the Salafist Group for Preaching and Combat (GSPC), which in 2006 allied itself to al-Qaeda.
Saifi, who was allegedly behind the 2003 abduction of 32 European tourists, was captured in Chad and returned to Algeria, where he is awaiting trial.
Anton Prohaska, a diplomat leading Austria's efforts in the region, has been in the West African nation of Mali for some time.
An Algerian website has reported that al-Qaeda in the Islamic Maghreb was in talks with Prohaska.
The Annahar website said the two Austrians were being held by Abdelhamid abu Zeid, an Algerian fighter, about 150km from Malian town of Kidal.
Relatives reported the pair missing when they did not return from a holiday 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.
Al Jazeera audio
The authorities began a search for the two tourists after Al Jazeera aired an audio tape, said to be from the al-Qaeda group, which linked the abduction of the consultant and nurse to the violence in Gaza.
The tape warned Western tourists to stay away from the Maghreb region of North Africa of which Tunisia is a part.
Joerg Haider, the governor of the southern Austrian province of Carinthia, said on Saturday that Libyan leader Muammar Gaddafi's son, Saif al-Islam Gaddafi, had held intensive negotiations with the captors and was very optimistic about their release.
On Sunday, in comments carried by the Austria Press Agency, Haider said the endeavour was a personal, secret initiative by Saif al-Islam that had not been prearranged with the Austrian foreign ministry.