Hamilton, who can clinch a sixth Formula One driver's title on Sunday at the US Grand Prix, had some critical words for Verstappen after the pair banged wheels during the opening lap of last Sunday's Mexican Grand Prix.
The Briton went on to win the race but later said that when racing Verstappen you have to give him more space in places where other drivers are "more respectful".
Ferrari's four-time world champion Sebastian Vettel backed Hamilton's assessment of the Dutchman's aggressive approach.
As the two world champions criticised Verstappen, who is famed for his bold overtaking manoeuvres, he shrugged off the attack claiming a psychological victory.
The Dutchman, who will be contesting his 100th career grand prix this weekend, said:
It only shows I am in their heads and I guess that is a good thing, From my side I don't need to dig into other people in a press conference.
He added: "First of all I think it is a bit disrespectful as well and I prefer to fight on the track which I love to do.
"I think from my side it is a bit of a silly comment to make because I think I am always a hard racer but fair.
"Of course it is easy to have a dig at someone but from my side it's fine."
Hamilton did not back away from his comments, dismissing any suggestion that his words were disrespectful.
"I was explaining a scenario so I don't think it was disrespectful in any way," said the Briton.
Verstappen made it clear there was no chance he would change his style any time soon, declaring that if you are not going to fight for victory, stay home.
"Of course I like to fight hard but on the edge, otherwise if they want me to stay behind it's also better to stay at home," said the 22-year-old.
Verstappen displayed plenty of that famous fight last year at the U.S. Grand Prix when he qualified 15th and clawed his way to a second place finish.
"You want to take the fight to them because that's what we are here for," he added.
We are racers, we are Formula One. I think we are the best out there and we do fight for victories because that's what I live for.