The latest headache for the FPOe -- part of the ruling coalition since late 2017 -- stems from alleged ties to a nationalist group, which made international headlines this week after receiving a donation from suspected New Zealand mosque attacker Brenton Tarrant.
Martin Sellner, who heads the Austrian branch of the Europe-wide Identitarian Movement (IBOe), confirmed Monday he had indeed been sent an unsolicited donation of €1,500 ($1,700), but insisted he had never met Tarrant.
However, Austria's government has threatened to disband the IBOe if an ongoing probe determined it was a terrorist group.
At a press conference earlier this week, FPOe leader and Vice-Chancellor Heinz-Christian Strache was quick to distance himself from the IBOe, insisting his party had "nothing to do" with the radical group, known for its anti-immigration stunts.
The focus on the FPOe's links with more radical elements will be particularly unwelcome ahead of Europan parliamentary elections, where the FPOe hopes to become one of many far-right forces across the continent to capitalise on anti-immigrant sentiment.
"It is a long-known problem (for the FPOe) -- it always has to distance itself from far-right fringe elements," political analyst Peter Hajek told AFP.
But Austrian media reports have now emerged documenting links between FPOe members and IBOe activists. The Standard daily on Thursday re-published a photo which has previously appeared in the Austrian media showing Strache sharing a restaurant table with several IBOe members.
Strache himself previously shared a video promoting the IBOe on his Facebook page, but said on Wednesday that at the time he thought they were a "counter-cultural youth movement against the left".
It is not the first time that the FPOe faces scrutiny since it became a junior partner in the government of conservative Chancellor Sebastian Kurz. Founded by former Nazis in the 1950s, the FPOe has in recent years sought to clean up its image, with Strache saying the party rejects all extremism.
In one of the most prominent cases last year, a lead candidate for the FPOe in a regional election was forced to stand aside after it was revealed that the student fraternity that he belonged to had previously published virulently anti-Semitic songbooks. He has since returned to politics for the party.
Analyst Thomas Hofer told AFP it was "a delicate situation for the FPOe". He said it was often a "balancing act" for the party to keep their conservative voters onside while still appealing to a more radical constituency.
The Freedom Party and the Identitarian Movement have in the past both railed against the so-called "Great Replacement," a conspiracy theory propagated in a 2011 book of the same title by French writer Renaud Camus.
Popular in white nationalist circles, the theory argues that white Europeans are being deliberately supplanted by non-white immigrants.
Tarrant's manifesto was also titled "The Great Replacement".
Analysts say the IBOe is unlikely to be disbanded unless links to terrorist activities emerge beyond the donation.
Sellner has been described as a central figure of the "identitarian" movement, which originated in France but has since spread across Europe and to the US.
On Thursday, Sellner said that his travel authorisation to the US had been revoked "based on my background", interfering with his plans to marry his fiancee there. British authorities also denied Sellner entry to the UK in March last year, saying his presence would not have been "conducive to the public good".
In July last year, Sellner and 16 other IBOe members were found not guilty by an Austrian court of charges of criminal association and hate speech. Two of the accused were, however, found guilty on lesser charges over the
storming of a university lecture hall during a refugee policy talk in 2016 and another stunt.
By AFP's Julia Zappei