The seven-time world champion managed to jump Leclerc in the first sector on the opening lap of the sprint race on Saturday, setting up a fight with Verstappen.
Hamilton managed to keep the reigning world champion in DRS range for a handful of laps during the early stages, but Verstappen soon moved out of sight and checked out in the lead, managing his way to a comfortable sprint victory.
Verstappen demonstrated by far the strongest race pace of the four frontrunning teams on Saturday, but he faces the challenge of starting from sixth on the grid for the Grand Prix following a track limit infringement during qualifying.
Addressing his hopes for the Grand Prix and the upcoming battle with Verstappen, Hamilton said: “That will be helpful for us at the front.
“Ultimately I think he will be breathing down our necks before too long with the pace that he had today, but I think it’ll open up for a good fight with Charles and Lando.
“We are all quite similar in pace so hopefully we can get to have a good battle tomorrow and if we can all keep Max behind tomorrow that’ll be awesome. But, if not, no worries.”
Despite the pace deficit to Verstappen in P1, Hamilton was positive about Mercedes’ performance at the Circuit of the Americas. “That was a fun race,” he explained.
“A good start down to Turn One, then a good battle with Charles. Then I was trying to get closer to Max but their pace is just undeniable at the moment.
“But I’m happy with just a little bit closer, we’ve still got a long way to be able to eek the pace that he was doing throughout the race, but nonetheless I’m really happy to be back on the podium.”