Jugend Rettet, Doctors Without Borders (MSF) and some other aid NGOs reject the new Italian code of conduct.
Italy plans to send warships close to the Libyan coast to pick up migrants.
The Italian parliament is debating the plan, already agreed by the government, which is aimed at stopping the flow of unstable, overcrowded migrant boats across the Mediterranean to Italy.
A tweet from Jugend Rettet (Youth Rescues) said the Iuventa "was not confiscated". "Our crew is not arrested. What happened is a standard procedure," it said.
Two Syrian migrants were taken ashore from the vessel, Italian media reported. Lampedusa, a tiny Italian island near North Africa, has struggled to house boatloads of migrants in recent years.
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