Austria says al-Qaeda militants holding two tourists have agreed to extend a deadline, set for midnight on Sunday, for their demands to be met.
Relatives reported the Austrian tourists missing on 1 March
Al-Qaeda in North Africa is demanding Islamists held in Algeria and Tunisia be freed in exchange for Andrea Kloiber, 43, and Wolfgang Ebner, 51.
The pair, who went missing while on holiday in Tunisia last month, are said to be being held in Mali.
A senior Austrian diplomat is in Mali seeking their freedom.
Austrian public broadcaster ORF says the aim of the Austrian authorities is to get the hostage-takers to drop their demands for the prisoners' release and concentrate on a ransom instead.
"The extension of the ultimatum is an enormous relief for us," Mr Ebner's son, Bernhard, told ORF.
On Thursday, the militant group gave Austria three days to secure the freedom of the two tourists.
The group posted images of the pair, whom it says it seized on 22 February, surrounded by militants in a desert.
They also warned Western tourists not to visit Tunisia and other North African countries, including Morocco, Algeria and Mauritania.
Relatives reported Ms Kloiber and Mr Ebner missing when they did not return from a holiday to Tunisia on 1 March.
Tunisia, a popular destination for European holidaymakers, has seen attacks on tourists by al-Qaeda in the past.
In 2002, a truck bomb outside a synagogue on the Tunisian island of Djerba killed 21 people, including 14 German tourists.