Austria's president has asked Alfred Gusenbauer, the surprise winner of the general election earlier this month, to form a new government.
Mr Fischer urged Mr Gusenbauer to form a stable government
Mr Gusenbauer, head of the Social Democrats, is now expected to enter talks with the centre-right People's Party over a possible grand coalition.
The People's Party of Chancellor Wolfgang Schuessel was knocked into second place in the 1 October vote.
The two men are due to set out their conditions in public later in the day.
They have nominated negotiation teams, who will try to overcome differences between the parties on tax policy, education and welfare reforms, privatisation, and a deal to buy 18 Eurofighter jet aircraft.
The People's Party signed up to buy the planes during its time in office, but the Social Democrats have said they want to scrap the deal.
Austrian President Heinz Fischer said he hoped the discussions would lead to "a stable government with a majority in parliament".