On Thursday Hamilton suggested that Red Bull's dominance is likely to continue despite the budget cap as the huge gap it enjoys affords it to shift its development efforts to next year's car earlier than its rivals.
The seven-time world champion, therefore, suggested implementing a summer deadline, which would be the earliest point from which any team could switch attention to its car design for the following year.
"It's not aimed at any one particular person or anything," Hamilton said at the Red Bull Ring.
"It's just obviously in my 17 years of being here, even before I got here, you see a period of time of dominance. And it continues to happen.
"I was really fortunate to have one of those periods that Max is having now. But with the way it's going, it will continue to happen over and over again. And I don't think that we need that in sport."
When Hamilton's idea was put to him, Verstappen dismissed it out of hand, saying the topic didn't crop up during the years that Mercedes was dominating.
"We weren't talking about this when he was winning and I don't think we should now," Verstappen told Sky Sports F1.
"This is just how Formula 1 works. When you have a competitive car, that's great, but at one point you have to look ahead to the next year, of course.
"It's normal people behind us say these kinds of things, but they should not forget how it was when they were winning themselves."
Mercedes has already spent a significant amount of its budget cap allowance on producing a vastly redesigned W14 for the Monaco Grand Prix, with Hamilton saying the team had finally "taken a step in the right direction".
When Verstappen was asked by Motorsport.com if Formula 1's budget cap was working, as Mercedes has had to pick its battles in its upgrade push, Verstappen replied: "But only the top teams have the money to develop everything at full speed, of course.
"Smaller teams can't, so then it's unfair again in that sense. You get a bit of the same story you had a few years ago.
"I don't know how [Mercedes] allocate their resources exactly, of course.
"Maybe they give up something else or save some money in other areas. I don't know, but I am not concerned with that at all."