A member of Burgenland’s regional government, Peter Rezar, has launched an attack on Chancellor Werner Faymann - and provoked a storm of protest from the SPÖ’s top politicians.
The conservative People's Party (ÖVP) won Sunday's vote with 27 percent, ahead of its ruling partners the SPÖ at 24 percent.
Rezar told the Kurier paper that the SPÖ’s poor performance “was largely down to the chancellor”, and predicted “problems” at the SPÖ’s national conference if Faymann failed to address the “core demands” of a tax on the wealthy, and a reduction of the lowest income tax rate by 25%.
Rezar also did not dismiss a coalition with the opposition right wing Freedom Party (FPÖ).
The head of the SPÖ in Vorarlberg, Michael Ritsch, also weighed in, saying that Faymann should show some backbone in negotiations with the ÖVP.
The chancellor, who has said he will never form a coalition with the FPÖ, dismissed Rezar's comments as irrelevant. "I don't take bad advice," he said.
SPÖ executive vice president Barbara Prammer described Rezar’s comments as "completely unnecessary" and “entirely the wrong response to the outcome of the EU election”.
Support for the FPÖ - which has been trying to set up a far-right group in the European Parliament with like-minded parties like France's National Front and Italy's Northern League - jumped up five points to 19.7 percent, compared with the 2009 EU election.
But the party, which has raged against an "anti-democratic" EU which encroaches on national sovereignty, failed to bump one of the ruling parties to third place and finish second as it had hoped.
The ÖVP and SPÖ - which have ruled Austria together or separately since the end of World War II - each take five seats in the incoming parliament.
The FPÖ will have four, up from two in the outgoing legislature, while the environmental Greens have three seats with 14.5 percent of the vote.
A new liberal NEOS group won 8.1 percent and gains one MEP.
The Alliance for Austria's Future, founded by the former far-right leader Jörg Haider before he was killed in a car crash in 2008, will leave the EU parliament after failing to scrape together even half a percentage point.