The health system had not lived up to its standards in the case of cancer victim Susie Long, Taoiseach Bertie Ahern told the Dáil.
Ms Long, who was buried on Monday, had to wait seven months for a colonoscopy to diagnose her bowel cancer.
Mr Ahern expressed sympathy with Ms Long's relatives.
"I know there are problems . . . Susie Long's death last Friday and the way she fought her case, and, obviously, felt very let down by the system.
"I followed what she said, the way her diagnosis was handled, whether it was a public or a private issue, which she felt strongly about.
"Very regrettably, the system did not live up to its standards in that case. That has clearly been put forward . . . "
Labour leader Eamon Gilmore said Ms Long was a very brave woman who had done the State a very good service.
"Her e-mail to Joe Duffy last January, which is published in today's Irish Times, is probably the most compelling narrative which we have seen about what is wrong with our health service."
She had described "the disgusting conditions" she had endured in the Mater hospital.
Mr Gilmore said the Taoiseach was wrong. "Susie Long did not blame the system; Susie Long blamed the Government."
He asked why Ms Long had to wait seven months for a test that could have been done in three days.
He also asked why public patients had to wait for months for the same service that private patients received in a shorter time.
Mr Ahern said it was deeply regretted that any patient referred to a hospital with possible cancer symptoms would be subjected to a delay in diagnosis.
"The Minister [for Health] has previously been assured by the HSE that any patient referred to St Luke's for a colonoscopy, and considered urgent by a doctor, would be given an urgent appointment and would be seen within a week or two."
Mr Ahern said urgent cases were forwarded directly to the medical consultants for prioritisation, and GPs were encouraged to make contact directly with them.
"That is how the system is meant to operate . . . That should have been the way for Susie Long's diagnosis . . . whether she was public or private."
Fine Gael leader Enda Kenny said he had also read Ms Long's e-mail, describing what she went through when waiting seven months for a simple colonoscopy.
"It seems to me as if the Government continuously now hides behind the HSE as being some remote agency, implementing Government policy without any reference to the human cost of what is going on."
Mr Ahern stressed the progress made in dealing with breast cancer, adding that breastcheck was available in 15 counties, in the eastern, northeastern, midlands and part of the southeastern and western regions.
Some 64,000 women were screened last year, he added.
He did not want to take away "from any of the genuine complaints or upsets caused to people . . . or, in some cases, fatalities". But he said patients receiving services, as distinct from those who wanted to be commentators, showed high satisfaction levels.
Seventy-six per cent of patients said they had been admitted to hospital immediately on being told they should be hospitalised; 11 per cent within a month; and 4 per cent within three months.
He said 83 per cent of hospital in-patients felt they had been treated with dignity and respect; and 64 per cent of in-patients and 58 per cent of outpatients rated their experiences as excellent.
