Thirty Pacific salmon have been found in nine Irish river systems since the first one was recorded in late June.
Fisheries chiefs said one of the most recent non-native fish to be captured was a mature male, which was ready to spawn when it was found on August 9 on the Erriff in Co Mayo.
Other catches of pink or humpback salmon, as they are also known, have been reported on the Foxford and Coolcronan fisheries on the Moy and the Owengarve river all in Co Mayo, the Galway Fishery and the Cong river on the Corrib system and the Drowes and Crana rivers in Donegal.
Inland Fisheries Ireland (IFI) appealed to anglers and the public to remain vigilant and report any Pacific pink salmon they see.
A similar issue has been reported on some fisheries in Scotland and there is no definitive explanation.
It has been suggested that some of the Pacific species have made their way south after "straying" from rivers in northern Norway or Russia.
They were introduced to some Russian fisheries in the 1960s and have colonised west along Arctic coasts.
The IFI said the potential impact of the species is unclear but their appearance in Irish river systems is a concern as they may impact on indigenous salmon populations in the future.
One fear is the potential introduction of parasites and pathogens not present in native salmonid fish and another is competition for food and space for juveniles.
The IFI said interbreeding with Atlantic salmon is unlikely as pink salmon spawn in late summer whereas Atlantic salmon spawn in winter.
The agency has set up a 24-hour hotline for anglers and members of the public to report pink salmon - 1890 34 74 24 or 1890 FISH 24.
Fisheries chiefs urged anglers who catch any of the pink salmon not to release them back into the water.
They want a record of the date and location of capture, length and weight of the fish and a photograph.
They also want the fish tagged and kept so they can run further tests to determine maturity stage and genetic origin.
Native to river systems in the northern Pacific Ocean and parts of the Bering Sea and Arctic Ocean, the fish have some distinguishing features including large black oval spots on the tail, very small scales much smaller than Atlantic salmon, and an upper jaw which extends past the eye.
They also have 11-19 rays on the anal fin and no dark spots on the gill cover.