The National Ambulance Service has said there has been no interruption of services after an overtime ban by around 500 staff commenced last Wednesday.
The organisation said they are monitoring the situation on an ongoing basis.
Earlier the Psychiatric Nurses Association claimed services are experiencing "significant" disruption and "potentially dangerous strain" due to the staff overtime ban.
The PNA says the dispute centres on the HSE's refusal to recognise them for negotiating purposes, or to deduct union subscriptions through its payroll system as it does for other unions like SIPTU which has negotiating rights for ambulance grades.
It has called on the Minister for Health Simon Harris to intervene and insist ambulance personnel should be permitted to join the union of their choice.
A response from the HSE is awaited.
Traditionally SIPTU represented the majority of the 1,800 ambulance personnel, but since 2010, the PNA claims around 500 of them have switched to its ambulance branch NASRA.
On 10 October, NASRA members commenced a work to rule, but escalated it to an overtime ban last Wednesday.
PNA General Secretary Peter Hughes blamed the HSE's "intransigent" and "reckless" decision not to allow ambulance personnel to join the union of their choice.
He said members were reporting that ambulance services are being stretched to the limit as the HSE has struggled to fill rosters and maintain crews in the absence of overtime from PNA members.
He alleged that the HSE had been putting together a "patchwork" of vehicles and crews to cover major gaps in rosters.
NASRA Branch President Sinead McGrath said that in the same week that Taoiseach Leo Varadkar called for restrictions on Christmas leave due to the pressures on the health service, the HSE was struggling to maintain ambulance services.
She said this was because of the HSE’s own actions in trying to force ambulance personnel into a union they do not want, while denying them the right to be members of a branch of the PNA.