OHM leader Laszlo Toroczkai told several hundred supporters, including members of vigilante groups, that the event was a "demonstration for order" and against "gypsy crime".
Toroczkai said Hungarians must be defended from "gypsy terrorists" and blasted other political parties for their "political correctness" as well as the authorities.
"We are here because the state failed to protect us," said Toroczkai.
Toroczkai, 41, was formerly a vice-president of the nationalist Jobbik party but left to form OHM after last year's parliamentary elections when Prime Minister Viktor Orban's Fidesz party won by a landslide and Jobbik's vote declined.
Mayor of a small town close to Hungary's southern border with Serbia where Orban erected a razorwire fence in 2015 to keep out migrants, Toroczkai accused Jobbik of abandoning its radical policies.
Between 2006 and 2009 Jobbik, whose then leader set up a militia group called the Magyar Garda, enjoyed a surge in popularity that helped it enter both the European and Hungarian parliaments.
The Magyar Garda held intimidating marches in Roma neighbourhoods around Hungary until it was banned in 2009.
"We have been afraid for days before Torockai's demonstration of what might happen," a member of the ethnic-Roma community in Torokszentmiklos told AFP without giving her name.
Last week Toroczkai, who is linked to several vigilante groups in Hungary, announced the formation of a new uniformed militia called the "National Legion" that he said would teach self-defence and basic military skills.
Toroczkai said the group wanted to continue the "idealism" of the Magyar Garda.
He has previously called for the banning of mosques in his town and said criminals should be sent to prison in Siberia.
OHM had planned to march through the town but police banned the parade.
The National Legion has been called the "new face of Hungarian fascism" by the Budapest-based European Roma Rights Centre non-governmental organisation.
Many in the ethnic-Roma community fear the return of militias to Hungarian streets and hark back to a wave of brutal, racially-motivated attacks a decade ago.
Six Roma including a five-year-old child were killed by neo-Nazis around Hungary between 2008 and 2009.
Often blamed for petty crime, the Roma, Hungary's largest ethnic minority, face widespread discrimination, poverty and exclusion from mainstream society.
"OHM has replaced Jobbik on the far-right, and is following the same strategy that Jobbik applied to gain national popularity," Bulcsu Hunyadi, an analyst with the Political Capital think-tank, told AFP.
OHM is taking part in the European Parliament election May 26 but is not expected to win any of Hungary's 21 allocated seats.
"Their aim is provocation, and getting publicity through these events, OHM deliberately timed this stunt on the Roma issue for the last phase of the election campaign," said Hunyadi.