London and Indian cities were among the top five destinations, report shows
The Briton, 47 points clear of Red Bull's Max Verstappen in the standings after seven races, lapped the high-speed Monza circuit - without spectators due to Covid-19 restrictions - with a best time of one minute 20.192 seconds.
Finnish team mate Valtteri Bottas, quickest in the sunny opening session in 1:20.703, was second on the afternoon timesheets but 0.262 slower.
"It felt like we made some improvement from P1 to P2," said Hamilton, who is two wins off Michael Schumacher's all-time record.
"It's quite a bumpy track so it's really about trying to get the right balance...I think we have a few more steps to make and I think it will be where I need it to be.
"But Valtteri's quick around here, there's not a huge amount of corners so it's often a lot closer than a place like Spa," added the 35-year-old Briton, who won comfortably in Belgium last weekend.
McLaren's Lando Norris - wearing a helmet with a pizza pattern - was third fastest after Renault's Australian Daniel Ricciardo had his time deleted for exceeding track limits.
The Briton was still unhappy with his day after suffering power unit problems.
AlphaTauri's Pierre Gasly was fourth on the timesheets with Verstappen, who crashed at the Ascari Chicane in the morning, fifth.
Ferrari had a difficult day at their home circuit, with Charles Leclerc and Sebastian Vettel both outside the top 10 in session one at the fastest track of the year.
Leclerc, last year's race winner from pole, moved up to ninth in the afternoon with Vettel 12th after a spin at Lesmo.
"The car is so hard to drive," complained Leclerc over the team radio at one point.
Verstappen's early incident brought out the red flags but the Dutch 22-year-old made it back to the pits and was soon on track again after repairs.
"Thankfully it was just a front wing. We're not flush with parts so we'll need it back from the marshals a bit later," Red Bull team boss Christian Horner told Sky Sports television.
"It's very high speed over there, so we're lucky to get away with the low-ish amount of damage that we did."
The Dutch driver's Thai team mate Alexander Albon was third fastest in the first session, but 14th after lunch.
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