Public Accounts Committee Chairman John McGuinness has said he is concerned at a decision by the St Vincent’s Hospital Group to reveal so close to Christmas that it pays salary top-ups.
It has emerged that the group, which runs St Vincent's Public and Private hospitals in Dublin, pays top-ups to six of its executives.
Chief Executive Nicholas Jermyn said it does not use charitable donations for the payments.
Mr McGuinness has said the PAC expects an explanation.
He said the "HSE, the Department of Health, and the Department of Public Expenditure and Reform have more questions to answer than the institutions under their control.
"It is hard to avoid the conclusion that a system of nudges and winks, which is growing bigger by the day, has now been uncovered, and responsibility for it is being passed around like a hot potato".
Meanwhile, the HSE Director General Tony O'Brien has requested a meeting with the group to discuss how it can move towards compliance with public sector pay rules.
The group had previously said it was compliant with the pay rules.
But in a letter to the HSE, Mr Jermyn disclosed the top-up allowances paid to the group's three most senior staff.
Mr Jermyn, whose HSE salary was more than doubled by private top-ups to almost €300,000, said the salaries were fully tax compliant.
He said no charitable donations were involved in the top-up payments.
The group's Director of Finance, Cormac Maloney, earns €140,876, which includes a private top-up of €32,544.
Its Director of Nursing, Professor Mary Duff, earns €96,405, including a top-up of €14,853.
Mr McGuinness said: "the HSE is now promising to ask questions of charities and St Vincent’s that it was in a position to ask four or five years ago. I would prefer if it explained why its senior managers were so lax in applying the rules and demanding transparency and accountability."
Officials from St Vincent’s will meet the HSE in early January and will come before the Public Accounts Committee on 16 January.