Hitachi want to build Advance Boiling Water Reactors (ABWR) at the Wylfa and Oldbury.
But the Office for Nuclear Regulation says the safety risk models put forward are not up to UK standards.
The ONR issued the firm with an official “regulatory issue” notice earlier in July.
It told the nuclear engineers they must address a “serious regulatory shortfall” in the safety plans.
Officials said plans were “insufficient to present an overall picture and thus, a reasonable understanding of the UK ABWR risk”.
The old Wylfa plant was dogged by technical problems and reactor 2 was shut down for ever on April 25, 2012.
Nuclear Electric were fined £250,000 with £138,00 costs for safety breaches following an accident on 31, July,1993.