Sixty-five of the fish were taken from the Delphi, Erriff, Kylemore/Dawros, Newport and Bunowen catchments in counties Galway and Mayo since August.
Inland Fisheries Ireland (IFI) said the licensing authority in the Department of Agriculture, Food and the Marine had confirmed tha t salmon farm owners have not filed any reports of escapes from cages.
The fisheries agency took the step of issuing a statement from its board, chaired by Fintan Gorman, amid concerns about the damage that inter-breeding can do.
"Inland Fisheries Ireland has been charged with the protection of wild Atlantic salmon and continues to have concerns regarding the impacts of fish farms on Ireland's precious wild fish," it said.
"The licencing regime and best management practice should provide assurance to the state that controls are in place that safeguard our heritage. This does not appear to be the case in this instance.
"Inland Fisheries Ireland supports sustainable fish farming but cautions against the renewal and/or award of licences where conditions are not being adhered to.
"The board recommends immediate strict enforcement and audit of existing licence conditions to ensure compliance and ultimately a sustainable resource for all."
It said the majority of the 65 escaped fish were caught by anglers, demonstrating that only a small proportion have been seen or intercepted.
Inland Fisheries' scientists are also running analysis on the captured fish in an attempt to identify their history and maturity and assess the risk to wild stocks.
Three tests so far were found to be mature males with the potential to spawn and impact the genetic integrity of native salmon stock, the agency said.