* All migrants to be brought to Italian ports

* Smugglers taking advantage of mild spring weather

* Three die in shipwreck off of Egyptian coast

* Libyan authorities detain hundreds of migrants (Updates number of rescued)

By Steve Scherer

ROME, May 4 (Reuters) - Nearly 5,800 migrants were plucked from boats off the coast of Libya and 10 bodies were recovered in less than 48 hours, Italy's coast guard said, in one of the biggest rescue operations this year.

Two weeks after nearly 900 boat people drowned in the worst Mediterranean shipwreck in living memory, the flow of people desperate to reach a better life in Europe has accelerated as people smugglers take advantage of calmer seas.

Seven bodies were found on two large rubber boats packed with migrants and rescuers plucked from the sea the corpses of three others who had jumped into the water when they saw a merchant ship approaching, the coast guard said.

Separately, authorities in Egypt said that three people died when a migrant boat attempting to reach Greece sank off its coast. Thirty-one people were rescued.

Italy's coast guard has coordinated the rescues by its own navy and coast guard, a French ship acting on behalf of the European border control agency, merchant ships, and one vessel run by the privately funded Migrant Offshore Aid Station.

DISAGREEMENT

Growing lawlessness and anarchy in Libya - the last point on one of the main transit routes to Europe - is giving free hand to people smugglers who make an average of 80,000 euros ($90,000) from each boatload, according to an ongoing investigation by an Italian court.

Libyan state news agency Lana said on Sunday authorities there detained 500 migrants in five boats off Tripoli and a further 480 migrants - from Sudan, Somalia, Eritrea and Ethiopia - were caught in a farm near the central town of Jufra, and another 170 were detained nearby.

Those rescued in the Italian operation were being brought to Italian shores, some already arriving at Lampedusa, Italy's southernmost island, and others at Trapani, Sicily. More were to be brought ashore overnight and on Monday.

Shocked by last month's record disaster, European Union leaders agreed to triple funding for the EU sea patrol mission Triton, but there is still disagreement on what to do with the people fleeing conflict and poverty in various parts of Africa and the Middle East.

Austrian Chancellor Werner Faymann said in a newspaper interview on Sunday that the EU should set up a quota system whereby member countries agree to take in more refugees in order to relieve some of the pressure on Italy, Greece and Malta.

But Austria's proposal is likely to face tough opposition from some members states, including Britain and Hungary.

Hungarian Prime Minister Viktor Orban said on Friday that EU states should be allowed to set their own rules on migrants, and that Hungary did not want any of them.

Mild spring weather and calm summer seas are expected to push total arrivals in Italy for 2015 to 200,000, an increase of 30,000 on last year, according to an Interior Ministry projection.

About 1,800 are estimated to have perished during the crossing already this year, the UN refugee agency said, while some 51,000 have entered Europe by sea, with 30,500 coming via Italy. ($1 = 0.8929 euros) (Additional reporting by Ahmed Elumami and Ulf Laessing, Editing by Robin Pomeroy and Phil Berlowitz)