Car parks and trails could be shut to stop people from visiting Snowdonia National Park after “unprecedented scenes” on Saturday, according to bosses.
There were so many people on mountain summits it was “impossible to maintain effective social distancing”.
Pen y Fan in the Brecon Beacons was also busy with visitors on Saturday.
Welsh ministers are considering their legal powers to force people to stay away during the coronavirus outbreak.
There have already been calls from local politicians and medics to encourage second home owners and caravan owners to stay away from Wales' holiday hotspots and adhere to guidance on social distancing to prevent the spread of Covid-19.
Snowdonia National Park Authority said the area “experienced its busiest ever visitor day in living memory” on Saturday.
Chief executive Emyr Williams said: “The area has been overwhelmed with visitors.
“More worrying still is the significant crowding on the mountain summits and trails making it impossible to maintain effective social distancing.”
The authority is calling on the prime minister and first minister to provide “stronger measures on unnecessary travel and social distancing, to ensure that we do not see a repeat of yesterday's scenes across Snowdonia”.
The park said: “If no further steps are taken we will need to take drastic measures to protect the communities and health services in north Wales, such as shutting down car parks and trails.”
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Boris Johnson has warned the NHS could be “overwhelmed” if people do not act to slow the “accelerating” spread of coronavirus, as he urged the UK not to visit loved ones on Mother's Day.
And Wales' Health Minister Vaughan Gething tweeted to say that he and First Minister Mark Drakeford were “actively considering our legal powers to directly intervene” due to concerns about the influx of visitors to Wales.