The navy said it was contacted by a Turkish merchant vessel about a "semi-sunken dinghy" around 40 nautical miles (74 kilometres, 46 miles) from the Libyan coast.
Territorial waters are usually up to 12 nautical miles out.
"Navy and coastguard naval units immediately set off to the area and managed to rescue 12 people. The search is continuing," the navy said in a statement.
A navy spokesman said it was not yet known how many people were originally on the boat or what countries they came from.
Most of the asylum-seekers are from Eritrea and Syria, but many are also economic migrants from sub-Saharan Africa.
