Verstappen and Hamilton came together on lap one when the Mercedes man tried to go around the outside of his rival at Turn 2, having been forced to avoid contact with Sebastian Vettel off the line.
While Hamilton recovered from the incident to win in Mexico, Verstappen dropped further down the order and then suffered a puncture when trying to move through the field by passing Valtteri Bottas in the stadium section.
Speaking post-race, Hamilton said he was "torpedoed" by Verstappen, although Bottas said this week that the situation had been "overblown".
Verstappen was less than impressed when asked about Hamilton's comments, which were backed up by Vettel, when discussing them ahead of the United States GP.
"Looking at Turn 1 and 2 in Mexico, I don't think that happened," Verstappen said.
"I think from my side it is a bit of a silly comment to make because I think I always hard race but fair, and I think it is just not correct.
"Of course it easy to have a dig at someone but from my side, it's fine. It's always positive when someone talks about you because it means you are in their heads.
"I just focus on my driving and that's enough said.
"I think that from my side it already shows that I'm in their heads. I guess that's a good thing.
"But from our side, I don't need to dig into other people in a press conference, because first of all I think it's a bit disrespectful as well, and I prefer to fight on track, which I love to do.
"And 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."
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