Cork County Council says it wants Iron Man management to provide it with a full report of Sunday's event in Youghal.
44-year-old Meath native Brendan Wall and 65-year-old Ivan Chittenden from Canada got into difficulty during the swimming portion of the event.
The Council says Iron Man has the sole responsibility for the management and coordination of the event, following the deaths of two men during Sunday’s race in Youghal.
Cork County Council says its responsibilities are limited to the organisation of road closure permits.
It aslo facilitates the use of some Council buildings and services, like waste collection.
The local authority says it does not have any responsibility for the management and operation of the event, or any decisions related to the races proceeding.
The council says the deaths of Brendan Wall and Ivan Chittenden may be the subject of a Coroner’s Inquest.
It is seeking a full account of the event from Ironman.
It says the Council will determine its future position as host sponsor once it has received and considered the report.
In a statement issued last night, Triathlon Ireland CEO Darren Coombes said the organisation is "reeling."
As per normal protocol, Triathlon Ireland officials conducted a safety assessment before the race began.
However, due to adverse conditions, they did not sanction the event.
An investigation is already underway into the deaths, with Triathlon Ireland adding that it would inappropriate to comment further at this time.