Verstappen leads the Mercedes driver by five points with eight rounds to go ahead of this weekend's Russian Grand Prix following a season full of drama between the duo, highlighted by their clash in Italy last time out.
Recalling his first title fight during his rookie season in 2007, seven-time champion Hamilton said: "I remember what it was like battling for my first championship and now I am fighting my 10th battle or something like that.
"I know the pressure that comes with it and the experiences that go with it, so I can empathise with that. I think what is important is we continue to race hard and fair.
"I have no doubts we can both be professional and learn from the past."
Verstappen "won't admit" to feeling pressure
Verstappen is in his seventh season in F1 despite only being 23 years old but it is his first championship battle.
Asked whether he believed the Dutchman would be feeling the pressure, Hamilton added: "Obviously, he won't admit to it so I am not going to make an assumption.
"But I am saying I remember what it was like when I had my first one and 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 is to be expected.
"There is a lot of pressure from working in a big team, a lot of self-expectation because the desire to win is huge.
"I was just saying I empathise and understand that and I know we will continue to grow from this."
What do you think?
Maybe at the last one or two races, but in this moment Max seems very relaxed and focused. Look at Zandvoort, all those Dutch fans, a whole country going mad only for him, the king and queen in the pit box an hour before the race but he didn't fall under pressure, he was sharper and more controlled than ever
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