Hamilton is looking to bounce back from his Belgium disappointment last week, in which he was unable to convert pole into victory at Spa, but his attempt to gain an early momentum in Italy was hindered by wet conditions, and the Brit ultimately managed just six laps in the morning practice session.
And with the second session boasting dry conditions, Ferrari showed the potential of their pace at their home Grand Prix as Vettel headed a one-two for the Italian squad. Hamilton, however, was just 0.287s behind in FP2, and the four-time world champion senses an opportunity to return to winning ways this weekend.
"We woke up to torrential rain this morning, which meant it was a less busy first session than normal,” said Hamilton. “We did a few laps but after that it was like having a day in the office when you don’t have too much work to do – I was even snoozing in the car at one point!
“But we did plenty of laps this afternoon in the dry and we could see that, like in Spa, we had a small gap to Ferrari on both the short and the long runs. My laps felt pretty good, but Ferrari were a little bit quicker today.
“We’re all working flat out right now in every part of the team, and we have work to do tonight as well – but there are some areas where we can see deficits, so I hope we can make a little step for qualifying.
“It has been a big battle for a number of races now, and they have had a small advantage since the middle of the summer, but we are pushing as hard as we can to overcome that.
“Although we are on Ferrari’s home turf, we have some great support out there and it’s always a boost to see that in the grandstands. It will be a very close fight tomorrow and, like every race weekend, we will be giving it everything we’ve got."
In the sister Mercedes, Hamilton's team mate Valtteri Bottas finished the day's two sessions 10th and 4th respectively, and the Finn believes the Silver Arrows can go even quicker when they compete for pole on Saturday.
"The conditions out there were quite mixed today with heavy rain in the morning and a dry afternoon,” said Bottas. “We did only one run in the morning on the intermediate tyres; Monza is a tricky place in the wet as it is difficult to find the right braking points.
"We seemed competitive in the wet compared to the cars who were out in similar conditions. Luckily the afternoon was dry and we could get some proper running in; the long runs were especially important as the race is expected to be dry.
"As expected, Ferrari seemed very quick in the dry. It’s not going to be easy, but we still have a few things we can improve for qualifying. Compared to Spa, the car felt better in the slow corners which is a good step in the right direction.
“The weather forecast for tomorrow is not entirely conclusive, so we need to be prepared for everything and get a lot of running done in FP3 no matter if it’s wet or dry."
Hamilton leads Vettel by 17 points in the drivers’ standings, and knows a victory at Monza's 'Temple of Speed' will boost his chances of a fifth world title.