"Our health system is under a situation of extreme pressure," Health Minister Marta Temido told reporters on Sunday afternoon after a visit to a struggling hospital.

"There is a limit and we are very close to it."

The health system, which prior to the pandemic had the lowest number of critical care beds per 100,000 inhabitants in Europe, can accommodate a maximum of 672 COVID-19 patients in intensive care units, according to health ministry data.

The number of people in ICUs with COVID-19 reached 647 on Sunday, according to health authority DGS.

The Portuguese Association of Hospital Administrators said the number of coronavirus patients needing hospitalisation was likely to dramatically increase over the next week.

Three days into a nationwide lockdown, the country of just 10 million people reported 10,385 new cases and 152 fatalities on Sunday, bringing the total number of infections to 549,801, with the death toll increasing to 8,861.

Portugal had the highest number of coronavirus cases in Europe per capita over the last seven days, according to a tracking website supported by Oxford University.

Most new cases were concentrated in Lisbon, where many patients at the city's public hospitals have already been transferred elsewhere, including to health units in the country's second biggest city Porto.

"We are already treating patients beyond our installed capacity," said Daniel Ferro, director of Lisbon's biggest hospital Santa Maria.

"And we are not the only hospital where this is happening."

The Garcia de Orta Hospital, across the River Tagus from Lisbon, said in a statement the hospital could soon enter a "pre-catastrophe" phase as it no longer has beds for coronavirus patients.

The military have already set up a COVID-19 ward at the Armed Forces Hospital in Libson to help ease the pressure.

Australian Associated Press