It was orchestrated activity that bore "all the hallmarks of fascism," Mr O'Connor claimed.
The Siptu president, who said the heckling came from Sinn Fein and United Left Alliance sign carriers, said he was seeking assurances from both parties that neither "condone nor acquiesces with such activity".
He said: "I am not alleging that either of the organisations approved of or condoned fascist activity of this kind. But the fact of the matter is that (it) is being carried on by people who are either associated with their organisations or elements who are very deliberately masquerading as such."
Using the term "fascist" to describe the heckling was not going too far if the activity was orchestrated, he said.
The Dublin Council of Trade Unions, which helped organise the demonstration in the capital, said it would seek to ensure future events were not "marred" by heckling.
Sinn Fein Dublin City Councillor Larry O'Toole said the party was not involved in the heckling, "nor does the party condone such activity."