It follows Betsi Cadwaladr University Health Board's decision to close four community hospitals and transfer care for seriously ill babies to England.
Council chief executives from across north Wales had a private meeting with board officials at Wrexham Guildhall.
Neither the board nor the chief executives were willing to comment following the meeting on Friday.
Hospitals at Blaenau Ffestiniog, Flint, Llangollen and Prestatyn will see services switched to 10 other locations after Betsi Cadwaladr University Health Board (BCUHB) confirmed their closures.
BCUHB has said it must overhaul services to meet challenges due to financial pressures.
It announced the changes last month, but its plans have met strong public opposition and protests.
Denbighshire council said its officers were seeking clarification and detail from BCUHB on three following areas:
"We are working closely with the CHC (community health council) and hope to develop the council's response in consultation with the CHC," said a spokesperson.
They added that the chief executive would be reporting back to councillors following Friday's meeting.
In response, a BCUHB spokeswoman said: "The chief executive and directors are meeting with the local authority chief executives to discuss issues regarding the health board's decisions.
"Issues raised by Denbighshire County Council are similar to those already raised by other councils.
"It would be inappropriate to comment on Denbighshire's concerns or others until after the meeting has been held."
The public opposition to BCUHB's decision continued on Monday when a motion of no confidence in NHS managers in north Wales was deferred by Conwy councillors after both sides agreed to hold talks.
The motion was proposed by three Colwyn Bay councillors from different parties after BCUHB's decision to close the community hospitals in Blaenau Ffestiniog, Flint, Llangollen and Prestatyn.
The deferred motion invited other north Wales councils to do the same and called upon the watchdog body the Community Health Council to use its power to refer the health board's decisions to the Welsh government.
A cross-party group of Assembly Members, including a Labour AM, have also called for Health Minister Lesley Griffiths to intervene.
Council leaders in Denbighshire say they have concerns about the impact of a health care shake-up in north Wales.