The Psychiatric Nurses Association (PNA) says the HSE should not be allowed to dictate which unions its staff want to join.
Over 500 ambulance service staff with the union are in the middle of a 24 hour strike in a row over union recognition.
The PNA is recognised by the HSE, but not its ambulance service branch.
General Secretary of the PNA, Peter Hughes, says they aren't afraid to take things further.
He explained: "We'll take it one step at a time - we'll plan weeks in advance, and then we'll determine.
"This is ongoing for 18 months now, and we have people here on a 24-hour strike.
"This is an escalation - it's not going to go away. It's time for the HSE to come and talk to us."
He added: "This is not a breakaway union, and therefore we believe the HSE should negotiate with us in relation to ambulance personnel members."
Today's 24 hour strike - which lasts until 7am on Saturday - follows a series of shorter strikes in recent months.
According to the PNA, further strike dates will be announced in the coming weeks.
The HSE has previously stated that they already recognise a number of unions for ambulance workers.
Officials claim recognising further organisations will not be good for industrial relations.