The Briton, who retired from the race in Belgium 12 days ago after team mate and championship leader Nico Rosberg hit the back of his car, missed an hour of the afternoon running as mechanics replaced sensors on his car.
Hamilton was still fastest overall on the day, with a best time of one minute, 26.187 seconds set before lunch. Rosberg was top of the afternoon timesheets with a best of 1:26.225, just ahead of his team mate.
“Hopefully I’ll be able to have the full session tomorrow and get some good running,” said Hamilton, who has had more than his share of mechanical problems this season while Rosberg has motored on.
“Monza is quite an important circuit to put the car at the front as it’s very difficult to overtake here. It would be great to have a trouble-free qualifying tomorrow.”
Jenson Button, Hamilton’s former team mate at McLaren, was second fastest in the morning in 1:26.810 with Rosberg – who has never been on the Monza podium – pushed back to third in 1:26.995.
Hamilton is 29 points behind Rosberg in the championship with seven races remaining and is determined to claw his way back against his German rival, who was punished by the team for the Spa collision.
“I didn’t feel 100 percent confident in the car, so I can’t be happy with today and I have a lot of work to do tonight with the boys,” said Rosberg.
Ferrari’s Fernando Alonso was fourth fastest in both sessions at the fastest circuit on the calendar, with team mate Kimi Raikkonen third in the afternoon.
“That was a very busy day, but a positive one. We made the most of every minute available to us in both sessions,” said Raikkonen, who has never won Ferrari’s home race.
Williams’ Valtteri Bottas was fifth in the second practice after a quiet morning and Button was sixth for McLaren, who last won a race in 2012.
Red Bull’s quadruple world champion Sebastian Vettel, last year’s winner at the ‘cathedral’ of Italian motorsport, was sixth and seventh while Australian team mate Daniel Ricciardo was 16th and 10th.
Ricciardo, as good as Italian to many of the home fans and chasing his third win in a row, was sidelined for some of the first session with a power unit problem.
“Obviously we want to be a bit further up, but I think we can chip away at it tomorrow, the Mercedes will be quick, but if we can sneak into the top five in qualifying then we’ll have a good crack at the race,” said Ricciardo.
“Getting temperature into the tyres is tricky, especially for the first timed lap.”
At the slow end of the field, Spanish driver Roberto Merhi made his debut appearance at a Formula One weekend and lapped faster than regular race driver Marcus Ericsson in the other Caterham.
Merhi handed the car back to Japanese Kamui Kobayashi, returning after being dropped by the team for Spa, for the afternoon and rest of the weekend.
Spanish reserve driver Daniel Juncadella also had a stint with Force India while Frenchman Charles Pic was handed compatriot Romain Grosjean’s Lotus for the session.
(Editing by Peter Rutherford, Pritha Sarkar and Toby Davis)