The Office of the Ombudsman received 3,190 complaints in 2013, down slightly on 2012.
However, Ombudsman Peter Tyndall said complaints to his office have increased already this year.
The largest number of complaints involved the Department of Social Protection, accounting for 491 complaints.
There were 310 complaints against the Health Service Executive.
Mr Tyndall said he was surprised at the low level of health complaints.
He said his office would be looking into why this was the case.
Mr Tyndall also called for the extension of his jurisdiction to include public services provided by private bodies.
He said at the moment if people have complaints about Irish Water there is no place to lodge a complaint.
Mr Tyndall said he has raised this with the Government and would like Irish Water to be included under his remit.
Mr Tyndall took over from Emily O'Reilly last year.
He said today he would like to see his office given constitutional status, which he said would reinforce the independence of the office, and increase public confidence in the work it does.