Germany's Der Spiegel and Sueddeutsche Zeitung published hidden-camera recordings, allegedly showing Freedom Party (FPOe) leader Strache promising public contracts in return for campaign help from a fake Russian backer.
After Strache resigned in a press conference Saturday, the head of Chancellor Angela Merkel's conservative CDU party Annegret Kramp-Karrenbauer said the affair showed “people like this mustn't be allowed to take any responsibility in Europe”.
“Far right populists are the enemies of freedom,” said foreign minister Heiko Maas from the centre-left Social Democratic Party (SPD).
Austria's conservative Chancellor Sebastian Kurz had been “irresponsible” to invite them into his government, Maas added.
Other parties used the opportunity to warn the CDU off potential alliances with German far-right outfit Alternative for Germany (AfD).
Votes later this year in Germany's former communist East look set to hand the party strong results that could make it hard to build regional coalitions without them.
Centre-right parties across Europe “should end their alliances with right-wingers and distance themselves clearly from the enemies of democracy,” Greens lead candidate for the EP Sven Giegold told the Funke newspaper group.
Although in the past they have presented themselves as bosom friends, there was no reaction to Strache's resignation from leading AfD figures by late afternoon Saturday.
Joint AfD leader Joerg Meuthen was in Milan for a gathering of nationalist parties organised by Italian deputy prime minister Matteo Salvini.
The FPOe's lead candidate for the European Parliament pulled out of the meeting after the scandal broke.