Coastguard and Maltese government officials launched a major search and rescue operation last night after news of the sinking.
Italian coastguard spokesman Marco Di Milla said an Italian ship was sent to help, while a Maltese armed forces aircraft was able to locate the wreckage.
Mr Di Milla later said that "a good number" of the estimated 200 people had been rescued.
He said the coastguard received a satellite phone call from the boat and was able to locate it based on the satellite coordinates.
A Maltese armed forces statement said that since the boat was in Maltese search and rescue waters, a Maltese aircraft was sent up and reported that the boat had capsized and that "numerous" people were in the water.
The aircraft dropped a life raft and a patrol boat soon arrived at the scene.
Malta's Prime Minister Joseph Muscat later said that at least three of the 27 dead are children.
Lampedusa is a popular of choice of smugglers ferrying migrants from Libya or Tunisia to Europe.
Last week, a ship carrying some 500 people capsized in the same area, killing more than 300 people.