The pair are locked in an increasingly intense title battle, Verstappen holding a five-point margin following the Italian Grand Prix.
There, neither title protagonist saw the finish in Sunday's race, though the points leader finished second in Sprint Qualifying to extend his advantage by two.
A crash at the opening chicane shortly after the pit stop cycle in Monza served only to up the ante in the championship battle.
In the clash, Hamilton ended the race with his Mercedes buried under the Verstappen Red Bull, the Dutchman awarded a three-place grid penalty for his part in the incident.
He will serve that this weekend amid suggestions he'll also take a further grid penalty for a new power unit.
That penalty is the expected result of his clash with Hamilton at the British Grand Prix, which resulted in an 51G opening lap impact at Copse.
“I'm just not putting any energy towards that, I'm just focusing on that you just put all the energy to moving forwards,” Hamilton said when asked if he was worried of further crashes with Verstappen.
“Naturally, we're battling for a championship.
“I remember what it was like battling for my first championship, and obviously I'm in my 10th [championship] battle or something like that, but I remember what it was like and I know the pressure that comes with it, and the experiences that you go with it so I can empathise with that.
“I think what's important is that we just continue to race hard but fair, and I have no doubts that we will both be professional and learn from the past.”
The 36-year-old burst onto the F1 scene with McLaren in 2007, and went within a point of claiming the championship in his rookie season.
He went on to claim the 2008 title in a similarly nail-biting climax to the season which, for a handful of seconds, looked to have seen Felipe Massa crowned champion.
While six titles have followed since, Hamilton has also been involved in unsuccessful tilts – such as 2010 when he was one of four drivers heading into the Abu Dhabi finale with a shot of victory.
Those experiences have left the Brit with an impression of what it takes to win a world championship, and the pressures his rival will find himself.
“Obviously he won't admit to it and so I'm not going to make an assumption but I'm just saying that I remember what it was like when I had my first one [championship battle],” Hamilton said when asked if their clash in Monza was evidence that Verstappen was beginning to feel the pressure.
“It definitely mounted up; it was difficult; it was intense.
“I was going through a lot of different emotions, I didn't always handle it the best and that's to be expected,” he added.
“There's a lot of pressure from working in a big team, there's a lot of self-expectation and pressure because the desire to win is huge.”