Greece's coast guard said the 28, including four infants and 10 older children, died when their wooden boat containing more than 125 people capsized near Farmakonissi.
The island lies midway between Samos and Kos, two of the favored targets for smugglers sending thousands of migrants and refugees daily to Greek islands off Turkey's coast.
Today's tragedy came just a day after two other boats capsized and at least five people, four children and a 20-year-old man, were presumed drowned. The coast guard said they still were searching for those bodies.
In Hungary, army engineers crowned the top of the planned 174-kilometer (109-mile) border fence with razor wire as the government warned that, from tomorrow onward, any asylum seekers caught breaking through the barrier would be arrested and charged with a criminal offense.
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This year, more than 175,000 have passed through Hungary from Serbia en route to Western Europe, and the government of Prime Minister Viktor Orban says it's determined to make Hungary a more difficult challenge, with deployments of troops and potential prison terms part of the deterrent.
Hungary's lawmakers have not voted yet on whether to back government plans to deploy more than 3,000 troops in support of border police, but dozens of soldiers already were patrolling the fence today.