But with the two set to race again this weekend in the Chinese Grand Prix, the 33-year-old Hamilton said he approached Verstappen in Shanghai in a bid to lower the temperature.
Hamilton lapped the 5.4km circuit in one minute, 33.999 seconds, 0.359 seconds clear of Ferrari's Kimi Raikkonen.
Lewis Hamilton and Mercedes have a point to prove at the Shanghai International Circuit after being outdone by Ferrari in the first two races of the season.
The top three finished the afternoon in the same order as they had ended the opening 90 minutes of practice. "Ferrari have got a very fast auto and there are millimetres between us". Red Bull were really quick on the long run.
"It's good to see all the times so close, but it means that we really need to bring our A game".
"We need everyone in the team to be on it throughout the weekend because it is a joint effort".
Sebastian Vettel admits his Ferrari auto has yet to hit the "sweet spot" despite a closely fought practice ahead of the Chinese GP on Friday.
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Hamilton is 17 points behind Vettel, who has won the first two races.
The former suffered no damage to his vehicle and went on to finish in third place, while the latter suffered a left rear puncture and damage to his diffuser and retired from the race two laps after the accident.
Mercedes have won the last four races in China and five of the last six and it is one of Hamilton's most successful tracks - he has also taken six pole positions.
Verstappen and Red Bull teammate Daniel Ricciardo both retired early last weekend in Bahrain, and they both had off-the-podium finishes in Australia: Ricciardo was fourth and Verstappen was sixth. But as soon as that all calms down a bit in the race, yeah, I was very confident, for example, before we went into the race to still move up a lot of positions, because I think the vehicle was definitely capable of just driving back to the podium.
Kevin Magnussen was seventh for the USA -owned Haas team ahead of the other Renault of Spaniard Carlos Sainz.
Hamilton was highly impressive in setting the fastest time in the first session on Friday, but the frontrunners closed in the second. Following pit stop problems for Ferrari and Haas this season, McLaren also hit trouble with Vandoorne pulling off the track at Turn 4 having noticed one of his wheels wasn't fitted properly.
Team-mate Lance Stroll, meanwhile, survived a spin.