Ross Brawn, the former team boss who is now F1's managing director for sport, presented images created by a graphic artist showing how the next generation might look after a rules revolution post-2020.
The sleek and aggressive cars featured bigger wheels with a more integrated halo head-protection system and simpler front and rear wings.
Mercedes driver Hamilton, 30 points clear of Ferrari rival Sebastian Vettel ahead of Sunday's Singapore Grand Prix, had sounded positive already after images began to circulate on social media.
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"I'm def (definitely) gonna be driving if cars look like this," the 33-year-old Briton said on his Instagram account. "Just please bring a V12 or V10 back."
Ferrari team principal Maurizio Arrivabene offered more of a verbal shrug, however.
"I was looking at the car presented a couple of days ago by Ross," he told reporters in a news conference after first practice.
"It’s a good exercise. I was asking our engineers what they thought about this, they said it’s a bit underwhelming in their opinion and it looks like an old ChampCar. But it’s an exercise."
Brawn said Formula One wanted drivers in cars that "young people want to stick up on their walls.
"I see no reason why we can't have exciting-looking cars. It frustrates me when a car in a video game looks better than a car that we're racing out on the track," he added.
"We're listening to what the fans want, we want to engage with their passion, we want them to feel that Formula One is listening to them."
Brawn said the main aim, however, was to have cars that could race more easily and overtake without losing performance at close quarters due to aerodynamic turbulence.
"The current cars lose up to 50 percent of their performance once they get to within one or two car lengths... which means they struggle to race each other," added the Briton.
"The prime purpose of what we are doing is to try and produce cars that are more raceable... at the moment we've got designs that only lose 20 percent of their performance."
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