ROME May 24 (Reuters) - Some 3,000 migrants were saved off the Libyan coast on Tuesday in 23 separate rescue missions, the Italian coastguard said in a statement.

The coastguard said this meant more than 5,600 migrants had been rescued from various boats and dinghies in the southern Mediterranean in just two days, with every ship in the area being called on to help with the complex operation.

Humanitarian organisations say the sea route between Libya and Italy is now the main route for asylum seekers heading for Europe, after a European Union deal on migrants with Turkey dramatically slowed the flow of people reaching Greece.

Officials fear the numbers trying to make the crossing to Italy will increase as weather conditions continue to improve.

Earlier this month, Italy said some 31,000 migrants, mainly from Africa, had reached the country by boat, slightly down on 2015 levels. However, the number of new arrivals has picked up markedly in recent days.

Most of those trying to reach Italy leave the coast of lawless Libya on rickety fishing boats or rubber dinghies, heading for the Italian island of Lampedusa, which is close to Tunisia, or towards Sicily. (Reporting by Crispian Balmer; Editing by Gareth Jones)