This follows the trouble that flared when scores of football hooligans converged on the Bourse in the centre of Brussels which has been turned into a memorial for the people killed and injured in the recent terrorist attacks on the city.
There were reports of racist and anti-Muslim chanting, Nazi salutes, as well as alleged harassment of Muslim women.
ENAR, which is based in Brussels, has now called on member states to "take steps" to prevent a possible escalation of violence resulting from calls for more protests.
A similar demo was due to be held on Saturday.
A statement issued by ENAR said, "Although Belgian authorities condemned the demonstration, it was allowed to proceed and granted police escort. The lack of strong reactions and concrete measures to prevent and sanction such manifestations of hatred and violence contribute to a climate of intolerance towards ethnic and religious minorities and migrants in Europe."
It goes on to say, "The need for strong actions is made all the more urgent by the fact that some individuals who publicly spoke out against the far-right protest have received death threats.
Public authorities and police forces have a duty to protect the population against all forms of violence and hatred."
The far-right group ‘Génération identitaire’ had called for an "anti-Muslim" demonstration in the Molenbeek district of Brussels on Saturday, fuelling fresh fears of more violence.
Although local authorities have indicated they will not allow the demonstration to take place in the district, ENAR wants the Belgian authorities and police to "ensure they protect the population, in particular those perceived as Muslim, against intimidation and violence by individuals on this day and any other day."
ENAR chair Sarah Isal said, "While member states are taking measures against radicalisation linked to violent Islamist political ideologies, not reacting appropriately to other forms of violent radicalisation, such as these incidents, has the potential to foster a sense of impunity for racist hate in Europe."
Isal further added "It also sends the signal that the ideas these groups promote are acceptable. In the current polarising context, political leaders must ensure that all members of society feel worthy of security, protection and well-being."
Elsewhere, the Socialist Mayor of Brussels Yvan Mayeur has condemned several Flemish politicians following Sunday's demo for far-right sympathies who "seemed bent on trouble."
"The spectacle could have been avoided," he said.
Mayeur is angry with his colleague Hans Bonte, mayor of Vilvoorde where the football "casuals" had massed ahead of their trip to Brussels.
He said, "It is scandalous that Bonte did nothing to prevent this."
He also criticised Belgian Home Affairs Minister Jan Jambon, a Flemish nationalist politician, saying, "He too did naught. This too is scandalous."
But Bonte, from Vilvoorde, defended the decision not to stop the men from travelling to Brussels, saying, "Otherwise they would have run riot here in Vilvoorde."
Christian De Coninck, spokesman for the Brussels police told Parliament Magazine, "The 340 hooligans had not applied for permission to come to Brussels but you can't stop these people. It's very delicate because there were so many of them. This is why we channelled them in the direction of the square outside the stock exchange building."