* Italy has proposed destroying boats used by traffickers

* U.N.'s Ban says to focus on security and human rights

* Ban due to visit Italy on Monday, discuss crisis

ROME, April 26 (Reuters) - There is no military solution to migrants drowning in the Mediterranean, U.N. Secretary General Ban Ki Moon said on Sunday, as European leaders search for ways to manage the flow of people leaving North Africa in rickety boats.

Ban's comments came a week after more than 700 people drowned in the worst shipwreck in decades of dangerous seaborne migration. The disaster has shocked the European Union into pledging more money for rescues.

In an interview with Italian newspaper La Stampa, Ban said the United Nations was ready to help tackle the problem. Asked about a proposal by Italian Prime Minister Matteo Renzi to "capture and destroy" the boats that traffickers use, Ban said the U.N. focused on security and protecting human rights.

"There is no military solution to the human tragedy playing out in the Mediterranean," Ban said. "It is crucial that we take a holistic approach that looks at the root causes, at security and the human rights of migrants and refugees, and have legal and regulated immigration networks."

EU leaders agreed on Thursday to triple funding for its naval searches in the Mediterranean. But it is still not clear how they will cope with longer-term issues, ranging from dealing with people smugglers to redistributing asylum seekers around the 28 EU nations.

Ban is due to visit Italy on Monday and meet politicians, including Federica Mogherini, the EU's foreign policy chief. Mogherini told La Repubblica newspaper on Sunday she would discuss with Ban the proposal to destroy the boats, saying it "does not mean preparing a military intervention in Libya".

EU leaders are also under pressure to manage housing migrants once they arrive on the continent without angering their voters, among whom opposition to immigrants has grown as years of recession strangled public spending.

Italy's location makes it a prime destination for would-be immigrants, most of whom are fleeing the Middle East and sub-Saharan Africa. Under the EU's Dublin treaty, migrants become the responsibility of the first European country they arrive in.

Many do not intend to stay in Italy, but asylum requests can take more than a year and the recession-hit state looks after many of them while they wait in reception centres.

Italian Interior Minister Angelino Alfano told Il Messaggero newspaper on Saturday that Italy was working on a substitute for the Dublin treaty, calling it "obsolete".

"We are working to construct a common system which goes beyond the Dublin treaty, which is now obsolete in practice, making the mechanism less rigid and more collaborative," Alfano said.

Last weekend's disaster came after a migrant boat collided with a merchant ship and then capsized. The Italian navy said on Sunday that 274 rescued migrants were due to arrive in the southern port of Taranto on Monday. (Reporting by Isla Binnie; Editing by Larry King)