These involved a Jeju Air 737-800 that underwent an emergency descent after the pilot forgot to engage cabin pressurisation, and a Jin Air flight that took off with an unsealed door.
The ministry is demanding enhanced safety measures such as more flight and ground crew per aircraft and better facilities at airports to service them.
Five LCCs now control more than half of South Korea’s domestic market, up from 10 per cent in 2008.
In other countries the rise of budget airlines has also been accompanied by disquiet over their safety standards - usually without any justification.
In Europe, for instance, Ryanair and easyJet have never suffered a major incident or accident-related death, while US operators such as JetBlue, Southwest and Spirit also have safety records comparable to, or better than full-service airlines.
Put simply, the reputational cost of a crash far outweighs savings from skimping on maintenance or training.
In Asia, though, budget airlines have a patchier reputation, due in large part to the atrocious record of several Indonesian carriers. Then again, their failings could be attributed to weak oversight by the national aviation authority – something Indonesia has moved to correct in recent years.
While Indonesia was once soft on safety, South Korea has been accused of heavy-handedness.
Failure to meet its new standards, for instance, can land LCCs with flight suspensions, route and slot withdrawals, and even grounding.
This follows a pattern established after an Asiana crash, due to pilot error, in San Francisco in 2013. Embarrassed Korean regulators banned the airline from flying to the city for 45 days, a punishment that met with protest from IATA.
“The imposition of further penalties by the state as an attempt to demonstrate oversight is disproportionate and unreasonable,” said DG Tony Tyler.
Rival Korean Air wanted the ban to be longer, but then became embroiled in its own scandal when vice-president Heather Cho was jailed over an air rage incident involving incorrectly-served nuts.
No doubt such fearsome regulation will see Korean LCCs shell out on new staff.