Details were revealed in an unpublished report by an expert group set up by the Health Service Executive.
The report said a situation could arise in which patients are placed in homes where inspection teams have raised serious concerns.
Mr Kenny told the Dáil that it was scandalous that 14 months after the Leas Cross affair, there was still no consistent system of inspecting institutions.
Taoiseach Bertie Ahern insisted that legislation, to be published soon, would put inspections on a statutory basis and establish a robust system of supervision of nursing homes.
Speaking on RTÉ Radio's Morning Ireland, Aidan Browne of the HSE said there was now a standardised policy of unannounced inspections of private nursing homes across the country.
Mr Browne said dedicated inspection teams would be in place as soon as possible.
The report says dedicated inspection teams in the HSE are the exception rather than the norm, and that very often inspections can be superseded by other demands on staff.
First report submitted to HSE
The Working Group on Nursing Home Inspections and Registration was set up in July last year, during the Leas Cross controversy.
Its first report, which has been submitted to the HSE, says there are very few dedicated inspection teams for private nursing homes.
In many cases, the team members are not in the same building, are spread widely across a health region and some are missing key experts.
The report claims policies and procedures on inspections vary between and even within former health board areas, and there is no consistency on who teams report to.
It says it is inappropriate for inspection teams to have serious concerns about a particular nursing home on record and simultaneously, another arm of the HSE continues to place public patients in the same home.
All statutory inspections of homes every six months should be unannounced and there needs to be more inspections outside of normal working hours, it recommends.
The report says there are concerns and inconsistencies in the notification of deaths, and that priority should be given to investigating.
