Fischer, who is known for his diplomacy and caution, had served as a science
minister and held various leadership positions in his party and in parliament
before initially winning the presidency in 2004.
Ferdinand Karlhofer, head of the University of Innsbruck's political science department, said the election results were a blow to the Freedom Party, which had hoped to position itself for key local elections in Vienna, Austria's capital, in October.
"The Freedom Party is coming out of this election with hefty minus points ... they didn't get the momentum they had hoped for,'' Karlhofer said.
"It really wasn't a fair election campaign, I think everyone saw that"
defeated Freedom Party candidate
Rosenkranz was the most visible figure during the presidential campaign, having previously sparked controversy by allegedly questioning Austria's strict law banning pro-Nazi speech and ideology.
She cried foul over media coverage of herself and her party after the results were announced on Sunday.
"It really wasn't a fair election campaign, I think everyone saw that,'' she said, claiming that both her and her family were the victims of a "witch hunt".
The 51-year-old mother of 10 children, whose husband used to be a member of a far-right political party banned for being too radical, had come under fire for her vague response to a question about Nazi gas chambers, but later clearly acknowledged their existence.
"Of course I condemn the monstrous atrocities, I've never done anything else," Rosenkranz told The Associated Press news agency in reference to the mass killings of mainly Jews by the Nazis during the second world war.
The far-right had been on an upswing in the general elections in 2008, with the Freedom Party and its rival Alliance for the Future of Austria winning a combined 27.9 per cent of votes.
Even in European Union elections last year, the two parties together took 17.74 per cent.
Heinz-Christian Strache, the Freedom Party leader who is running for mayor of Vienna, cited the low turnout for Rosenkranz's poor showing.
"This is no occasion for joy," Strache, who had initially predicted a 35 per cent share of the vote for his candidate, said.