The move could help to reduce mounting tensions between Italy and its EU partners over the large numbers of migrants who arrive in Italy but are not registered here and then travel on to northern Europe.
If they are not registered in Italy, neighbouring countries like Austria and France and popular destination states like Germany and Sweden do not have the option of sending them back to Italy.
In theory they should be able to do this under the EU's Dublin convention rules governing asylum claims.
The Italian move follows talks on Wednesday between Interior Minister Angelo Alfano and EU migration commissioner Dimitris Avramopoulos in Sicily, where most migrants arrive and are processed at "hotspot" reception centres.
"With this we will now have hotspots at sea," Alfano said.
It was not clear if the policy will be applied systematically - migrants picked up at sea are often in a traumatized state and asylum seekers from Eritrea notably generally refuse to have their prints taken because they want to make their applications elsewhere.
Italy was warned last year by the European Commission that it must make its registration procedures more efficient.
But Italian officials say the country cannot cope alone with the migrant influx.
More than 350,000 people from all over the world have reached Italy on boats from Libya since the start of 2014, as Europe battles its biggest migration crisis since World War II.
Alfano said that after problems in 2014, the process of identifying migrants was now working "100 percent".
With Austria on the verge of introducing anti-migrant checks at its border with Italy in the Alps, there is mounting concern in Rome that the country's overcrowded reception facilities could soon have to deal with tens of thousands of additional asylum seekers.
Italian Prime Minister Matteo Renzi warned Austria not to go ahead with the border closure. "It would be a flagrant breach of European rules, as well as being against history, against logic and against the future."
The tensions have given added urgency to attempts to find a lasting solution to the crisis and Italy is pushing a plan to introduce NATO naval patrols off Libya in time for the peak summer season for people smuggling.
Modelled on an existing NATO operation in waters between Turkey and Greece, the plan has been backed by US President Barack Obama and is expected to be approved by alliance leaders at a summit in Warsaw in July.
Italy has also proposed offering an EU-funded scheme to offer African countries cash to cooperate with the fast-track repatriation of migrants deemed to have no claim to asylum in Europe.