The dispute over Georgescu's candidacy is firing up tensions both at home and abroad.
A small group of his supporters smashed pavements and set rubbish bins ablaze in Bucharest on Sunday, while Elon Musk, a key adviser to US President Donald Trump, branded the decision to bar Georgescu "crazy".
Romania, a NATO and EU member, has found itself at the centre of a dispute between Europe and the Trump administration over the nature of democracy.
US Vice-President JD Vance said Romania's annulment of its election in December amid allegations of Russian interference meant it did not share American values.
Russia denies interfering in Romania's presidential vote.
"We go together all the way for the same values: peace, democracy, freedom," Georgescu, appearing alongside two political allies, said in a video posted on Facebook, confirming he would appeal to the Constitutional Court against the ban.
Georgescu also urged supporters to shun violent protests "like (those) we saw yesterday evening".
Georgescu submitted his presidential bid on Friday.
Romania's central election authority said on Sunday it had decided to bar Georgescu's candidacy, saying it was inadmissible after the Constitutional Court's annulment of the December vote.
Challenges to decisions by Romania's central election authority must be filed within 24 hours.
The Constitutional Court should rule on Georgescu's appeal by Wednesday.
Analysts have said it is unlikely that the top court will allow Georgescu to run again for the presidency.
The court set a precedent in October when it blocked the candidacy of another far-right candidate, arguing that her anti-European, pro-Russian views made her unfit for office.
If the court upholds the central election authority's decision, three opposition ultranationalist parties, which hold 35 per cent of seats in parliament and which backed Georgescu's previous presidential bid, risk having no candidate in the May election.
George Simion, leader of the opposition Alliance for Uniting Romanians, met Georgescu on Monday.
Asked before the meeting if he was considering submitting his own candidacy, Simion told reporters: "We wait to see what Mr. Georgescu will say. We are not ruling out any options, but we are not speculators."
Simion said he had been in contact with JD Vance's team in the past 24 hours, but not directly with the Trump administration.
He did not elaborate.
Georgescu is under criminal investigation on six counts, including membership in a fascist organisation and communicating false information about campaign financing.
He has denied any wrongdoing.
