People should be banned from travelling to second homes and caravan parks should be shut down, Plaid Cymru leader Adam Price has told the first minister.
In the letter to Mark Drakeford, Mr Price called for action, echoing calls from other politicians and GPs.
Travel is one of many restrictions in place since the coronavirus outbreak.
The Welsh Government has warned second-home owners and caravanners they could face action by ignoring advice not to travel unnecessarily.
Mr Price said concerns had been raised about "a large scale population shift" into generally rural areas.
His letter added: "I am asking that you now take urgent steps to avoid unnecessary additional pressure on our health and social care system at this difficult time."
Calls have previously been made for people not to come to Gwynedd, which has more second homes than any other county in Wales.
Driving through Barmouth and it’s absolutely rammed like it’s a hot summers day. Loads of people walking about, queuing up for ice cream and flying kites. What are people not understanding? This is going to be disastrous.— Seren (@vineyser) March 21, 2020
But now neighbouring Anglesey council has told all tourists to stay away from the island until the outbreak is over.
The main concern is putting extra pressure on health services.
"There's clear advice for people to avoid unnecessary travel and going to your caravan on the weekend doesn't strike me as necessary travel," Health Minister Vaughan Gething said.
"We're asking people to be responsible. And I really hope we take that advice seriously because I certainly don't want our healthcare system in any part of Wales or indeed the UK to be overwhelmed by people moving around.
"And that's something that of course is within Wales as well. There are plenty of people who have caravans and second homes in some of our coastal areas.
"We are of course taking it seriously and if we need to act, we are prepared to use the powers that we have, as we already demonstrated last night with the measures we took."
On Saturday, there were reports of social gatherings at Pen Y Fan in Brecon Beacons, Snowdonia in Gwynedd, and seaside resorts around Wales.
Anglesey council leader Llinos Medi said she was left with "no other option but to urge visitors and tourists, including those who own second homes, to stay away".
She added: "We have seen a recent influx of visitors coming to stay in caravans or second homes on Anglesey.
This is a #pandemic not a Bank Holiday. What bit of non-essential travel means coming from across the UK, potentially with CV, to climb Snowdon; strip local shops of food; put Mountain Rescue at risk at least twice today & pressure on a limited NHS; & ignoring social distancing? pic.twitter.com/R420HM0ELS— Claire Turner (@ClaireTTweets) March 21, 2020
"They will undoubtedly put an immense extra strain on essential public services, including the NHS, which are already under tremendous pressure.
"They must consider the implications of their actions on the people of Anglesey."
The calls have been echoed by Ynys Mon MP Virginia Crosbie and Clwyd West AM Darren Millar.
I live a stone’s throw away from one of the biggest caravan parks in Europe. It’s crazy that 1000’s of tourists are still being allowed to travel to their caravans/second homes in #Wales It needs to stop now, before the #Welsh #NHS is over run with new infections! #CoronaCrisis https://t.co/UhmMolWRmX— Dean John 🏴🇪🇺⚽️ (@deanindiejohn) March 21, 2020
Ms Crosbie said: "After several discussions with ministers yesterday, today I wrote to the prime minister asking him to re-affirm to the people of the UK that non-essential travel includes taking unnecessary holidays during a time of national crisis."
Darren Cornish, a lead GP at Criccieth, Porthmadog and Blaenau Ffestiniog surgeries, wants to see holiday parks closed.
"I don't think people understand the gravity of the situation," he said.
Given concerns over the impact of tourists on local NHS services and food supplies, Welsh Ministers must issue guidance to holiday parks and tourism operators in Wales. Sign up for further updates. #Covid19UK #Covid19Wales #CoronavirusUK #CoronavirusWales https://t.co/Vv10v3pI5M— Darren Millar AM 🏴 (@DarrenMillarAM) March 21, 2020
"If people do travel, a number will be bringing the virus with them and expediting the process.
"We need to close these campsites."
Meanwhile, Chris Lloyd, from North Wales Mountain Rescue Association said people were being "irresponsible" going up mountains during the coronavirus outbreak.
"We clearly weren't expecting a flood of people on Snowdonia today because we are actually trying to reduce the risk of team members having to deal with people who are possibly infected.
"The message is simple - don't go on the mountains if you have the virus or have been self-isolating because if you need to be rescued, mountain rescue may not be able to help."
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