The announcement from Save the Children followed a similar move by German aid group Sea Eye, which also cited security concerns.
The humanitarian organization said it had asked Libyan authorities to adhere to the internationally recognized legal obligation to rescue boats in distress, and to allow this to take place in global and Libyan waters.
A spokeswoman for SOS Méditerranée, which operates the Aquarius rescue ship, toldReuters, "Any attempt of interference would endanger the lives of people in need of protection".
Sea Eye said it has helped save about 12,000 lives since April 2016, and cautioned on Sunday that the retreat of aid groups from Libya's coast was putting lives at risk.
"European states and Libyan authorities are jointly implementing a blockade on the ability of people to seek safety", Brice de le Vingne, MSF's director of operations, said. "This is an unacceptable assault on people's lives and dignity".
The Guardian reports that the Libyan Coast Guard has become "increasingly more aggressive" in its patrols of the waters off its coast.
Humanitarian organisation Médecins Sans Frontières (MSF) has chose to suspend its search and rescue operations in the Mediterranean following threats from the Libyan coastguard.
The organisation's founder Michael Buschheuer explained: "The reason for this is the changed security situation in the Western Mediterranean, after the Libyan Government announced an indefinite and unilateral extension of their territorial waters - in connection with an explicit threat against the private NGOs". The MSF medical support team will continue to assist the rescue capacity of the Aquarius vessel, run by SOS Méditerranée, which is now patrolling in worldwide waters. "It would be irresponsible towards our crews".
De Maizière's remarks come as Italy renews its push to allocate Libya and other parts of Africa with additional resources to stem migration flows across the Mediterranean.
The number of migrant arrivals in Italy in July was down dramatically on the same month past year, suggesting efforts to train up and better equip Libya's coastguard may already be having an impact.
Italian Foreign Minister Angelino Alfano said in a newspaper interview on Sunday that Libya's growing role in controlling its waters was curbing people trafficking and producing a welcome "readjustment" in the Mediterranean.
Italy has struggled with the wave of refugees and migrants arriving at its coast.
The number of migrant arrivals in Italy in July was down dramatically on the same month a year ago, suggesting efforts to train up and better equip the North African country's coastguard could already be having an impact.