The humanitarian group said the rescue coordination center operated by Italy's coast guard had informed it Friday that the Libyan threats pose a security risk. The group added that Libyan authorities declared their own rescue area, extending into international waters, the same day.
Doctors Without Borders says its medical crew will keep working from a ship operated by another aid group while its vessel, Prudence, is not involved in migrant rescues.
The Italian government agreed last month to dispatch a naval mission to assist the Libyan coast guard with anti-smuggler patrols. Hundreds of thousands of rescued asylum-seekers, many of them fleeing poverty in Africa, have been brought to safety in Italian ports in recent years.
The government also has pressured rescue groups to sign on to rules that would forbid them from entering Libyan waters to save migrants without specific authorization and require them to agree that armed Italian judicial authorities may board their ships.
Italy is requiring groups operating rescue ships to subscribe to the rules or risk not being allowed to dock in Italian ports. Doctors Without Borders has refused to endorse the rules, while some other humanitarian groups have given their approval.
Critics of the new policies say they could put lives at risk by delaying rescues in Libyan waters. They also contend that if the Libyan coast guard blocks smugglers' boats, migrants will be returned to inhumane conditions, including beatings and forced labor, in Libyan detention centers.
"If humanitarian ships are pushed out of the Mediterranean, there will be fewer ships ready to aid persons before they drown," Doctors Without Borders Italy President Loris De Filippi said in a statement. "And whoever doesn't drown will be intercepted and brought back to Libya, which we know to be a place of absent legality, arbitrary detention and extreme violence."
A Spanish humanitarian group, Proactiva Open Arms, said the Libyan coast guard ordered its rescue ship to move north and fired warning shots last week when the vessel was involved in search-and-rescue work outside of Libyan territory.