Conditions in overcrowded migrant camps on Greek islands are reaching crisis proportions, a senior UN official said Thursday, urging Athens to take action.

“Greece is facing a crisis of reception, not a refugee crisis," UN Deputy High Commissioner for Refugees Kelly Clements said after a four-day visit to Greece.

"The government needs to tackle this by accelerating action to find accommodation, end overcrowding, boost services and improve living conditions," she said from the flashpoint island of Lesbos.

The call came as EU leaders met in Brussels in a desperate effort to overcome divisions and reach a concerted policy on migration.

Lesbos has the highest concentration of migrants and refugees in Greece, and conditions are worst in the camp of Moria where 6,000 people live, according to UN figures, about triple the nominal capacity.

Most there wait months for their asylum applications to be processed. Living conditions are squalid and violent flare-ups common.

The overcrowding saps the residents' health and also means that the vulnerable -- including women and unaccompanied minors -- are often in close quarters with non-family members.

The local community leader Nikos Trakellis briefly went on hunger strike earlier this week to draw attention to the issue, protesting over the sewage and garbage from the camp, and frequent fires endangering local property.

Greece is harbouring over 58,000 refugees and migrants according to the UN, and dozens continue to arrive on a daily basis from neighbouring Turkey.

Just the islands opposite Turkey have around 15,000 refugees and migrants.

Over 13,000 have arrived in Greece by sea since the beginning of the year, the UN agency says.

At present, some 2,700 people are waiting to relocate from Lesbos to the Greek mainland after being granted approval by authorities.

Thanks to a 2016 deal between Turkey and the EU, the influx has been drastically reduced from the thousands that arrived daily at the height of the refugee crisis that overwhelmed the EU in 2015.