Children made up the majority of passengers, with 146 minors, 102 men, and 28 women, one of whom was pregnant, were rescued.
About 500 migrants were rescued, but seven people died, the navy said.
She said the training effort, which would probably begin on European Union naval ships in global waters, "will be very important to control Libya's territorial waters, together with our Libyan partners, as well as to control the migrant influx". Fears have also grown that weather conditions will mean more people attempt the unsafe 300 km crossing to the island of Lampedusa in Italy.
A large wooden fishing boat overcrowded with migrants capsized off the coast of Libya, the Italian navy said on Wednesday, with some 562 people rescued and five found dead.
Incredibly, more than 6000 migrants have been rescued from the Mediterranean in just two days.
IS militants in Libya are not directly involved in people smuggling, he said, but do extort the traffickers who operate in their territory, he said.
The boat sent a distress call from 18 nautical miles off the coast of Libya, which was received by Italian navy patrol vessel the Bettica.
More personnel and boats will be needed, he said, but further resources will have to be set aside in Brussels first and then "in three or four months the Libyans will be able to act autonomously".
On Friday, Mogherini said the European Union and the North Atlantic Treaty Organisation could cooperate in training Libyan coastguards in curbing arms smuggling in the Mediterranean.
The Bettica went on to pluck another 108 migrants from their dilapidated vessel in a second rescue operation.
No breakdown of the nationalities of the people rescued was immediately available.
Officials say that there is no sign yet of Middle Eastern refugees switching to the Libyan route to Europe following moves to restrict access from Turkey via the Greek islands.