Doctors are monitoring Labour Senator Jimmy Harte on an hourly basis as he continues to fight for his life.
The Donegal politician remains in a critical but stable condition after a freak fall left him with serious head injuries.
It is understood the 55-year-old remains in an induced coma at Beaumont Hospital, while tests are ongoing to establish the extent of damage caused.
A Labour Party spokesman said the father-of-four's family are staying close to the hospital should there be further developments in his condition.
"He is being monitored very closely and his family will be keeping an eye for any results from tests that should be coming through," he said.
"He was admitted to hospital in a very, very serious condition and he remains critical.
"His family have been encouraged and heartened by the good wishes that he is receiving from the people within the Labour Party, and indeed other political parties, and from the wider public."
The senator, from Letterkenny in Co Donegal, was found collapsed on the street at Newmarket Square in Dublin's south inner city at around 3am on Saturday morning.
He was taken to Beaumont Hospital, which specialises in head injuries, with a fractured skull.
He underwent emergency surgery on Saturday to relieve swelling to his brain and has been under constant watch in the intensive care unit since.
There has been no major change to his condition so far today.
Gardai have viewed CCTV footage and interviewed witnesses who were in the area of Newmarket Square where he was discovered.
They are satisfied the injuries were sustained as a result of an accidental fall rather than any assault.
The insurance broker had been attending the Republic of Ireland v Latvia football international friendly at the Aviva stadium in Ballsbridge, south Dublin, earlier in the evening.
Labour leader Eamon Gilmore is among many party colleagues who have been in touch with the Harte family to pass on their best wishes and who are keeping a close eye on his condition.
Mr Harte, who runs his own insurance brokerage, is from a well-known Donegal family who have been involved in politics for generations.
He is also known as a keen sportsman, who has run 12 marathons in recent years and raised more than 30,000 euro for charities.
A former chairman of Finn Harps FC, Mr Harte played inter-county soccer and GAA in his younger years.