It is the closest Italian territory to the North African coast and the centre is struggling to cope as it only has a capacity for about 400 people.
At least twelve boats were intercepted on Sunday night with a total of 691 people on board who had left the ports of Zuwarah in Libya and Sfax in Tunisia.
It comes as a Spanish NGO ship is heading to the port of Livorno to help 117 migrants rescued in the central Mediterranean.
The government’s programme for the transfer of migrants to other locations was immediately set in motion and it is planned that about 200 will be taken to the port of Porto Empedocle, in Sicily and the Diciotti ship of the Coast Guard will also relocate a further 600.
It comes ahead of a delegation of the European Parliament’s Civil Liberties Committee on Tuesday to find out more about the rescue and reception situation in Lampedusa.