The spectre of coronavirus striking severely overcrowded refugee camps in Greece has hovered menacingly for months.

International aid organisations, human rights groups and doctors have sounded the alarm. With the spread of the pandemic, calls for action to prevent impending medical catastrophe have become shriller. In Aegean islands on the frontline of the crisis, health carers speak of days gained, not won.

But an outbreak of the disease in two facilities near Athens has intensified concerns over the estimated 36,000 men, women and children stranded on remote isles opposite the Turkish coast.

Installations on Lesbos, Samos, Chios, Leros and Kos – at six times over capacity, sprawling, wretched and congested – where social distancing, and other precautionary measures are an impossible privilege, offer fertile ground for Covid-19.

“Time is on nobody’s side,” said Dutch physician Steven van de Vijver, the driving force behind an online petition urging EU leaders to bring refugees to safety by agreeing to take them in from Greece. Since its launch last week, more than 6,000 European doctors have signed the appeal.

“It’s going to require superhuman force and a lot of luck now to stop this potentially lethal virus penetrating island camps,” he said. “At this point, I would say it’s almost impossible that it won’t happen.”

After two weeks working in Moria, the squalid and notoriously overpopulated holding facility on Lesbos, De Vijver realised it was an illusion to think that, in such conditions, Covid-19 could be kept under control.

“It would be a miracle and it’s dangerous to expect miracles to happen. Coronavirus doesn’t respect borders or barbed wire. People, camp workers, go in and out all the time, and with them the risk of the virus,” he said.

It would be a miracle to stop the virus entering the camps and it's dangerous to expect miracles to happen Steven van de Vijver

Greek authorities recognise that they are in a race against the clock. Detection of the disease in camps in Malakasa and Ritsona – among 30 refugee facilities on the mainland – has put them in uncharted territory. Malakasa was placed in quarantine on Sunday, hours after an Afghan refugee began displaying symptoms of the virus; Ritsona, 75km north-east of the capital, was sealed off after 23 African asylum seekers tested positive on Thursday.

Speaking to the Guardian after ordering the first lockdown, Manos Logothetis, the migration ministry’s general secretary in charge of asylum seekers’ reception, said: “It’s the first case of coronavirus in a reception centre and, yes, we are testing our responses. We’ve quarantined the entire area and taken steps to isolate those with the virus. It’s not been easy, there’ve been protests.

“Food has been brought by the International Organization for Migration, which is running the site, along with translators and cultural mediators. Testing will continue.”

The outbreak was traced to a 19-year-old Cameroonian woman found to be infected after giving birth in an Athens hospital.

Ritsona is relying on food handouts from the International Organization for Migration. Photograph: Yannis Kolesidis/EPA

“All the rest who have tested positive are asymptomatic,” said Logothetis, a doctor himself. “I found that surprising, but as in all the camps Ritsona’s population is young. Most are under the age of 40 which is why we believe they’ll be able to ride this out.”

However, many disagree. A surge in migrants from Turkey, even before the epidemic arrived in Europe, had increased concerns over the cramped and unsanitary conditions of reception centres in Greece.

Increasingly, NGOs have voiced fears over lack of access to testing, medical facilities and basic services, including water stations and taps. Calls for the evacuation of refugees to other EU countries have also soared amid evidence of the devastating effect coronavirus is likely to have on an already vulnerable population.

Holding facilities on the mainland are generally managed better; refugees are accommodated in containers and pre-fab houses, in stark contrast to the tent cities on the Aegean isles that have long borne the brunt of the migrant and refugee crisis.

“It is not a matter of ‘if’ but ‘when’ coronavirus strikes the camps,” said Sanne van der Kooij, a Dutch gynaecologist who has similarly volunteered in Moria multiple times. “I do not have a good feeling. I was last in Lesbos in February and worked at the local hospital where pregnant refugee women are moved to give birth. There were only six ICU beds and the care was very poor. The bed linens were filthy and the Greek doctors and nurses were clearly overwhelmed by the extra work.”

Although so far confirmed coronavirus cases have been reported only among local people on Lesbos, refugees requiring emergency medical help run the risk of contracting the virus, she said. “In the hospital for example. That’s where so many will be at threat of coronavirus infection. And then the spread inside [the facility] will be very difficult to stop.”

Most asylum seekers in the island camps are from Syria, Afghanistan, Iraq and Africa. Unable to leave because of a containment policy determined by the EU, they have found themselves in limbo, trapped on the outposts opposite the Turkish coast until their asylum requests are processed.

Almost 35,000 European health workers and other citizens have also backed the doctors’ petition calling on EU governments to comply with an accord struck with Turkey in 2016 under which each member state agreed to take in a fixed number of refugees. Although it is central to a pact aimed at curbing migratory flows, the resettlement pledge was never fulfilled.

Greece has, so far, had relative success in keeping transmission of the disease under control, announcing fewer than 2,000 confirmed coronavirus cases and a death toll of 76.

But health officials warn that the coming weeks are critical.

“The EU will have blood on its hands if it continues to look away,” warned De Vijver, speaking from Amsterdam where most of his patients in the city’s main hospital are now suffering from coronavirus.

“There are 22,000 people in Moria: men, women and children all packed into an area that is a fraction of the size of Hyde Park. Scabies, pneumonia, diarrhoea are rife,” he said, adding that conditions had deteriorated markedly since NGOs and volunteer medics had left the island following violent attacks by far-right vigilantes last month.

“I was astounded to see that this terrible situation had caused 80% of the complaints we were dealing with. Politicians in the EU have a moral obligation to take these people in,” he said.

Greece’s centre-right government has described the camps as “ticking health bombs”.

So far this year about 10,000 asylum seekers have been moved from the islands to the mainland – including 1,785 to closed, pre-deportation centres – according to the UN refugee agency. Plans are afoot to transfer another 600 people – 300 elderly refugees and their dependents – to hotels in Athens.

Reflecting restrictive measures enforced across Greece to combat Covid-19, authorities have allowed ATMs to be installed in the island facilities, as part of a wider lockdown on the camps.

But Logothetis accepts that in the event of a “mass coronavirus outbreak”, health officials on Lesbos would be hard pushed to cope. “In an ideal world we would rent a big venue, keep it warm and kit it out with beds. That I hope will be the next phase of our emergency operational plan because with so few ICUs on the island we don’t have the capacity to withstand the pressure if a lot of people were to get sick at the same time.”

The pandemic has effectively stopped any prospect of voluntary returns of migrants under a EU-funded scheme announced last month. Citing coronavirus concerns, the asylum service is also sputtering. Though operational again following Athens’ suspension of applications in response to Turkey’s abrupt decision to relax border controls and allow refugees to head to Europe, the service is not receiving new requests.

Doctors have warned about the consequences of a widespread outbreak in the island camps. Photograph: Manolis Lagoutaris/AFP

Hopes of resettling around 1,600 unaccompanied children to other parts of Europe have also dwindled. Officials say member states now want additional health checks, “which will take time”.

With the spectre of gridlock, Athens has come under increased pressure from the EU to relocate asylum seekers to the mainland. But that, says Greece’s migration minister Notis Mitarachi, is practically impossible without adequate accommodation.

Addressing the EU parliament’s home affairs committee as police moved to lock down Ritsona, he reiterated what prime minister Kyriakos Mitsotakis has said repeatedly: Europe should do more to help because Greece “cannot resolve this crisis instantly and alone”.

It is a refrain echoed by Logothetis. “We need support and we need to share the burden,” he said. “If each of the other 26 EU member states agreed to take in 2,000 people, our problem would be more than settled. I’d be able to empty the islands in a day.”