The total number of people on waiting lists to be treated, or seen by a doctor, now stands at over 707,000, the highest number recorded.
The latest figures issued by the National Treatment Purchase Fund are for May and are up by more than 6,200 on the previous month.
The overall figures have been rising every month since autumn of last year, except for a small dip in February.
A small drop has been recorded in one area, the number of people waiting for inpatient, or day case treatment, who have been waiting for a date.
The number of patients, meanwhile, waiting to be seen at an outpatient clinic for the first time to be assessed by a consultant has increased by more than 4,300 to 511,904.
The hospital with the biggest outpatient waiting list is Galway University Hospital with 39,048 patients waiting.
Other hospitals with large waiting lists include the Mater in Dublin with 38,641 patients waiting and Waterford University Hospital with 36,027 patients waiting.
These are patients who have been referred by their GP to be seen at an outpatient clinic.
In a statement, Minister for Health Simon Harris said he welcomed the fact that there had been a reduction in the number of people waiting for hospital operations or procedures.
The inpatient day case waiting list figures for May are showing a reduction of more than 800 compared with April, and a reduction of 7,000 compared with May 2017, the minister said.
Mr Harris added that a number of high volume procedures are being targeted for treatment by the NTPF.
The minister said that in May, there were decreases in the number of patients waiting for certain procedures such as angiograms, varicose veins, and cystoscopies.
Mr Harris said he recognised the outpatient waiting list "remains a significant challenge", which he said the Health Service Executive and NTPF were working hard to address.
"A draft Outpatient Action Plan for 2018 has been presented to me and work is ongoing to finalise the plan which is focused on improving overall use of resources to tackle long patient waiting times and to ensure timely access to treatment and care for patients," he said.