At least three people, including a child, died when a boat carrying more than 90 migrants sank off the Greek island of Rhodes on Monday, police said.

The sailing boat carrying the migrants ran aground on rocks off the Aegean island on a crossing from Turkey, a police spokesman told AFP.

Most of the survivors had to be pulled from the sea, and police fear the death toll could grow as they try to determine how many people were on board.

Greek authorities said they rescued 93 migrants, 30 of whom were subsequently hospitalized.

The boat crash happened a stone's throw from shore, so was caught on film and video by witnesses.

One harrowing clip shows about a dozen migrants, some wearing life jackets, clinging to a chunk of boat debris before being hauled on to land.

There has been a surge in migrants trying to reach Greece's Aegean islands from the Turkish coast in the last 10 days.

More than 700 migrants arrived on the island of Lesbos last week.

Greece's radical left government, which has taken a less hardline attitude to migrants than its predecessors, appealed to local authorities last week to help accommodate the latest wave of refugees.

Greece lacks the means and the infrastructure to adequately cope with the growing number of migrants landing on its shores and crossing its borders, most of them en route to northern Europe.