Sixteen survivors were recovered, and the tiny East African nation's coast guard continued a search and rescue operation after Tuesday's accident, the U.N. said in a statement. Witnesses said large waves caused the overloaded boats to tip over about a half-hour after departing.
An 18-year-old survivor told the migration agency he had boarded one of the boats with another 130 people, including 16 women. There were no immediate details on the second boat.
Thousands of migrants from the turbulent Horn of Africa region set off every year from Djibouti to cross the Bab al-Mandab Strait for the Arabian Peninsula with hopes of finding work in rich Gulf countries.
The vast majority of the migrants are Ethiopian, young and male, the migration agency says.
The crossing is dangerous, with smugglers in some cases forcing migrants overboard before reaching their destination. Other boats have been fired on as they approach Yemen, where fighting continues between pro-government forces backed by a Saudi-led coalition and Houthi rebels.
"This tragic event demonstrates the risks that vulnerable migrants face as they innocently search for better lives," said the migration agency's Djibouti chief of mission, Lalini Veerassamy.
The agency's Missing Migrants Project says at least 199 people have now drowned off the Djibouti coast near Obock, where the latest capsizing occurred, since 2014.
The Obock region, home to the port city of the same name from where the boats set sail, is unusual in that it sees people passing in both directions -- boatloads of Yemeni refugees fleeing war cross vessels carrying African migrants seeking better opportunities.
In 2017, 100,000 migrants arrived in Yemen, with many aiming to head north to find work in Saudi Arabia and its neighbours.
"The number of new arrivals arriving in Yemen has been continuously increasing since 2012, despite the deepened insecurity and violence following the war that erupted in March 2015," the IOM said in its 2018-20 regional migration response plan.
"Arrivals peaked in 2016 when over 117,000 arrived in Yemen," it added.
This migration continues even though Yemen is facing one of the world's worst humanitarian crises.
U.N. officials say 80 per cent of the population -- 24 million people -- are in need of aid and nearly 10 million are just one step away from famine.
IOM said that most of the journey migrants take to Yemen is by foot, walking across the scorching desert regions of eastern Ethiopia, Djibouti and northern Somalia.
Once they arrive in Yemen they could face torture, blackmail, sexual abuse or forced labour.
In 2017, some 2,900 people, mostly Somalis and Ethiopians, fled the dire conditions they had found in Yemen back to Djibouti.
The sea crossing itself has repeatedly proven perilous.
Last year, at least 30 migrants from Somalia and Ethiopia believed to be headed for Djibouti drowned when their boat capsized off Yemen amid reports of gunfire being used against those on board.
In August 2017, dozens of migrants from Somalia and Ethiopia died after human traffickers forced them off two Yemen-bound boats and into the sea.
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