Several MEPs have urged the European Parliament to stop paying a €600,000 (£474,250) grant to an alliance of far-right, anti-EU groups.
The rules say that blocking the cash is only possible if 25% of the parliament's 751 MEPs, from at least three political groups, request it.
Critics call the Alliance for Peace and Freedom (APF) a "neo-Nazi" movement.
German MEP Manfred Weber, head of the main centre-right group, is one of those who wants the funding stopped.
The APF was launched in 2015. Its deputy chairman is Nick Griffin, formerly an MEP who led the British National Party (BNP).
An Italian veteran of the far-right, Roberto Fiore, chairs the alliance.
He was convicted in absentia in 1985 for links to NAR, a fascist group blamed over the 1980 Bologna train station bombing, which killed 85 people. He now leads a party called Forza Nuova (New Force).
Another deputy to Mr Fiore is Artemis Matthaiopoulos from Greece's Golden Dawn, an anti-immigrant party which sports Nazi-style symbols. Party members have been accused of serious crimes including murder, and some went on trial last year.
The APF also embraces the German National Democratic Party (NPD), whose leader Udo Voigt is an MEP. Germany's Constitutional Court is considering whether to ban the NPD.
Respect for EU values?
A source at the parliament told the BBC that grants to European parties were usually transferred at the end of March, and "should money have been paid unduly, it will need to be reimbursed".
If enough MEPs object, a parliamentary committee will assess whether the APF acts in accordance with EU principles, namely "liberty, democracy, respect for human rights and fundamental freedoms and the rule of law".
As head of the powerful European People's Party (EPP) group Manfred Weber should be able to get the required 25% of MEPs united against the grant, the source said.
Last month Mr Weber wrote to other parliamentary group leaders and Parliament President Martin Schulz, saying there should be no such EU support for "some of the most radical and militant right-wing extremist parties".
Similar complaints against the APF were made by MEPs Marita Ulvskog (Sweden) and Daniele Viotti (Italy).
In its programme the APF says it stands for "promoting our common Christian values" and giving a voice to citizens who are "alienated from the democratic process" in the EU.
The APF has forged links with officials close to Syrian President Bashar al-Assad and has condemned Nato, alleging that Western politicians are fomenting "Russophobia".
The far-right grouping expressed solidarity with Serbian nationalists commemorating the 1999 Nato bombing of Serbia. "The memories of the many innocent victims of Nato missiles and of the Islamist death squads of Albanians and Arab Jihadis in Kosovo are still raw," it said on Facebook.
Mr Griffin, who was expelled by the BNP in 2014, argues that Western leaders are fulfilling a "neo-con/Zionist" agenda, which helps Israel.