"A big part of Fiat's premium strategy is based on brands like Maserati and Alfa Romeo," Elkann said at the plant in Grugliasco, where there was also a shareholder meeting celebrating Maserati's 100th anniversary.
The two brands "aim to produce unique cars capable of putting together the most advanced technical excellency with the Italian style loved around the world," he said.
Fiat sold 2,367 Maseratis in the first quarter of the year - 331.1 percent more than in the same period in 2013 - and it is aiming for 50,000 models a year by 2015.
There was a marked increase during the quarter in Maserati sales in Italy and other parts of Europe where the market had been badly hit by the economic crisis and the number of models sold also went up 341.7 percent in the United States.
Alfa Romeo is also aiming to ramp up production to 400,000 vehicles a year from 2018 from 74,000 in 2013.
Fiat as a whole sank into the red in the first quarter, losing €319 million mainly on costs associated with its takeover of US car maker Chrysler.
Vehicle shipments were up 9.1 percent from the year-earlier quarter to 1.1 million units, and net revenues gained 12.3 percent to €22.1 billion.
Gains came in sales in North America and the Asia-Pacific region, and revenues from luxury brands nearly doubled, including Maserati, where revenues were four times higher in the quarter.