BRUSSELS--European Union foreign policy chief Federica Mogherini will meet United Nations Secretary General Ban Ki-moon and Italian Prime Minister Matteo Renzi on Monday, as the EU works to respond to a refugee crisis.

Monday's meeting will take place on the Italian Navy ship San Giusto off the coast of Sicily, Ms. Mogherini's office said on Saturday. She will meet high-ranking U.N. officials and other international partners on Tuesday in New York and will travel to Washington for talks with U.S. Secretary of State John Kerry on Wednesday.

EU leaders tasked Ms. Mogherini last Thursday with pursuing options for taking on criminal gangs who have organized the trafficking of people on dangerous sea journeys from the Libyan coast to Europe. Hundreds of migrants have died in recent days in such crossings, prompting a response from the 28-nation bloc.

In addition to stepping up funding for possible search and rescue missions, EU leaders are looking at an initiative that would allow authorities to capture and destroy the boats used by smugglers. That is likely to be a limited military operation and could require backing from the U.N. Security Council.

Ms. Mogherini is expected to gauge the prospect for U.N. support for such an operation on Tuesday. Ms. Mogherini's office said she would also be in contact in the coming days with the U.N. High Commissioner for Refugees, Antonio Guterres, and the head of the African Union commission.

Write to Laurence Norman at laurence.norman@wsj.com

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