The migrants, who were bound for Italy, were picked up off the western city of Sabratha.
Mr Grandi praised the efforts of rescue groups including the Italian coast guard, Frontex (the European Border and Coast Guard Agency) and non-governmental organisations, saying they had saved tens of thousands of lives. And an estimated 200,000 are expected to arrive in 2017.
"Europe needs a comprehensive and co-ordinated migration and refugee response that takes into consideration the right to seek asylum and provide legal and safe alternatives to the boat smugglers", he says, and adds that: "Safe returns or other options should be handled quickly and with dignity for those concluded not to be in need of global protection".
Seconds later, Kellie Osman, 21, from Sierra Leone, was shot by one of the smugglers.
Separately, police said three Nigerians were detained in Sicily on Thursday and face charges of allegedly killing, torturing and sexually assaulting other Africans while they were trapped in Libya awaiting a passage to Italy. Larger wooden boats carrying several hundred migrants are rarer.
Former French Prime Minister Manuel Valls says France's Socialist party "is dead" and that he wants to run under the banner of President-elect Emmanuel Macron's political movement in June's parliamentary elections.
Small bulldozers could be seen Friday clearing up the now-empty warehouses by the Belgrade bus station that have become a symbol of the migrant plight.
It highlighted the confusion in the crowded waters as desperate migrants try to reach a better life and authorities scramble to deal with the chaos.
Germany has launched a new website created to help encourage migrants to return voluntarily to their home countries.
More than 6,000 migrants have set off on boats into the Mediterranean since late last week, bringing the total this year to more than 43,000, according to the U.N. High Commissioner for Refugees.
Germany is trying to speed up the asylum process for those likely to be allowed to stay like Syrians fleeing war, and quickly return home those with little hope of asylum.