Leclerc, whose home Monaco race follows next week, led both sunny sessions at Imola's Enzo e Dino Ferrari circuit and ended with a best time of one minute and 15.906 seconds.
George Russell lapped second fastest for Mercedes in the first session, 0.104 seconds behind and also on soft tyres, but McLaren's Oscar Piastri was closest to Verstappen in the second with a gap of 0.192.
Ferrari's Carlos Sainz was third in session one and RB's Yuki Tsunoda was a surprise occupant of that slot in session two for his team's home race.
Verstappen, winner of four of six races this season, lapped fifth and seventh fastest respectively after going off track in both sessions.
"A difficult day. Just difficult to get a good balance and just not really feeling comfortable in the car, moving around a lot," he said.
"We have a few things that we have to look at because today definitely just bad, just not comfortable. Also, the long run was really bad, so definitely a few things that we have to improve if we want to be competitive tomorrow."
The Dutch driver, who was 0.250 off the pace in first practice and 0.541 slower than Leclerc in the second, complained over the radio of a lack of grip as his car bounced across grass and gravel at Acque Minerali.
"It's so difficult everything, man. This time suddenly the front grips up a lot, I almost spin," reported Verstappen, who also appeared angry with Mercedes' Lewis Hamilton getting in his way, at one point.
Seven-times world champion Hamilton, racing in Italy for the first time since his move to Ferrari next season was announced, spun his Mercedes onto the grass with 22 minutes left in session one but was able to continue.
The Briton was fourth in the later stint.
McLaren's Lando Norris, winner in Miami last time out for his first career victory, was eighth and 12th.
Williams' Alex Albon brought out red flags briefly when he pulled over early in the opening session, with the team saying the engine shut down after he went over a kerb.
British teenager Oliver Bearman was back in a Formula One car after standing in for an unwell Sainz in Saudi Arabia, this time replacing Kevin Magnussen at Haas for the first practice session as part of six such outings this year.
Bearman did his push for a race seat next season no harm with the 15th fastest time, and team mate Nico Hulkenberg was last on those timesheets.
"Again, he (Bearman) has done another very, very good job. He's so calm. He understands what he needs to deliver each session, each run, each lap," said Haas team principal Ayao Komatsu.
"And he's able to absorb the information so quickly, you know, either from himself from the previous lap or the engineer's feedback. So again, I can't really fault him today. Great job."
