A third person has died in a week in the Moria refugee camp on Greece's Lesbos island, raising alarm about the grim winter conditions in overcrowded facilities that critics have denounced as deplorable.

The dead man is believed to be about 20 years old and from Pakistan, a police official on the island said. Another man who shared his tent was critically ill and taken to hospital.

The death at the island's Moria camp follows those of a 22-year-old Egyptian and a 46-year-old Syrian who shared a tent and died days apart. Greek media reported they had inhaled fumes from a heater, but authorities would not confirm or deny that.

Greece's migration minister Yannis Mouzalas ordered an investigation into the deaths, the causes of which remain unclear.

Steps would be taken "to make the situation more manageable", he was quoted by the Athens News Agency as saying.

"We wonder how many deaths it will take for the government to wake up," said Stavros Theodorakis, leader of the small centrist party To Potami.

At least 3,000 refugees and migrants are living in Moria, a hilltop former military base where conditions have deteriorated as they await, for months, word on their future.

The United Nations refugee agency and other international organisations have urged Greece to improve conditions at its overcrowded facilities.

'Wanton loss of life'

"Something has got to give. We cannot tolerate this wanton loss of life," said International Rescue Committee Greece director Panos Navrozidis, acknowledging that conditions in Moria did not meet humanitarian standards.

READ MORE: Concern over EU plans to send refugees back to Greece

As a mid-winter freeze gripped parts of the country earlier this month, thousands of asylum seekers endured sub-zero temperatures. Summer tents on Lesbos were weighed down by snow.

Across Greece, more than 60,000 refugees and migrants - most from Syria, Iraq and Afghanistan - have been stranded since last March, in formal or makeshift camps, which US-based group Human Rights Watch has described as "deplorable and volatile."

"We don't know yet how they died, but we do know the thousands stuck on the Greek islands have been suffering horrendous conditions in the cold, trapped by the failure of the EU to offer protection and dignity," said Gauri van Gulik, Amnesty International's Europe director.

Earlier this month, Germany announced its intent to start deporting newly arrived asylum seekers back to Greece, despite a five-year suspension of such returns due to the poor conditions in Greek camps.

That decision came just a month after the European Commission recommended that member countries return refugees and migrants who first entered the EU in Greece back to that country.

The announcements have been widely condemned by rights groups and humanitarian organisations.