Debt-laden Greece has seen a six-fold rise in the number of migrants landing on its shores over last year, the U.N. said Friday.

"In recent weeks, sea arrivals from Turkey have been averaging some 600 people a day," said Melissa Fleming, a spokeswoman of the U.N. refugee agency UNHCR.

"In the first five months of 2015, we've seen over 42,000 people arriving by sea to Greece" against 6,500 in the same period in 2014, she said. The total number of arrivals last year was 43,500.

There has been a surge in migrants trying to reach Greece's Aegean islands from the Turkish coast recently, mirroring the swell in perilous crossings from northern Africa to Italy.

Late last month, the European Union asked member states to admit 40,000 asylum seekers from Syria and Eritrea over the next two years to help overwhelmed Italy and Greece.

"More than 90 percent of the people arriving in Greece are from refugee-producing countries, principally Syria (over 60 percent of arrivals this year), Afghanistan, Iraq, Somalia and Eritrea," Fleming said.

She said conditions were "dire" for the new arrivals with the three existing reception facilities vastly overstretched and "no regular provision of food or drinking water."

"In some of the islands, local volunteers have organized themselves spontaneously and have asked local restaurants and bakeries for food donations to distribute to the refugees who are sleeping rough or in unused buildings," Fleming said.

The refugee agency called on "EU institutions and agencies to further enhance the support provided to Greece" to cope with the influx.

She said the numbers were expected to swell even more as it was just the start of summer, a season when Mediterranean crossings surge.