Mercedes, the sport's dominant team, said they were working hard to fix Rosberg's car before qualifying for the final European race of the season.
Rosberg, who managed just three laps and did not set a time, leads Hamilton by 29 points with seven rounds remaining and has had few mechanical problems while the Briton has had more than his share.
Hamilton had problems with his car's electronics on Friday but was untroubled on Saturday, with the sun shining at the historic track near Milan, and wrapped up practise with a fastest time of one minute 25.519 seconds.
Ferrari's Fernando Alonso lapped second fastest at his team's home track, in 1:25.931, with Williams drivers Valtteri Bottas and Felipe Massa living up to expectations in third and fourth places.
Red Bull's Daniel Ricciardo, winner of the last two races, was ninth with four times world champion Sebastian Vettel sixth.
Toro Rosso's Russian rookie Daniil Kvyat was eighth but is set to take a 10 place grid penalty for Sunday's race after having to exceed his allocation of five power units for the season and using a sixth.
(Reporting by Alan Baldwin, editing by Amlan Chakraborty)
Share
