Around 50,000 people arrived in Greece in July alone, the organisation says.
Greece's leader said the country was unable to cope, and called for EU help.
Separately, Italian police arrested five suspected traffickers over the deaths of about 200 people after a migrant boat sank on Wednesday.
They included two Libyans, two Algerians and a Tunisian, held on suspicion of multiple murder and people trafficking.
Survivors have said that traffickers used knives to slash the heads of African migrants and belts to thrash Arabs to keep them in the hull. (+ BBC videos) » | Friday, August 7, 2015
