Talks at the Workplace Relations Commission to end the dispute will resume this afternoon.
A planned strike was called off this week as unions and the HSE seek a resolution.
Finance Minister Paschal Donohoe is reluctant to pay the HSE support staff in case it sparks other pay claims.
He said: If the money was there and it was easily available we wouldn't be where we are at the moment.
He continued: "I'm not going to agree to any kind of a change that causes everything around me to unravel because the consequences of that for public pay match some of the difficulties that we were just debating with the National Children's Hospital.
"If I start adopting a position that is different to that, the discussions that are underway in the World Place Relations Commission will come to an end."
