George Russell was the fastest in Friday practice at the Miami Grand Prix, the most competitive showing by far this season.
Charles Leclerc was 0.106 seconds quicker than Russell.
Verstappen failed to set a time while Perez and Hamilton were ahead of Mercedes.
Fernando Alonso was fifth fastest for Alpine.
Carlos Sainz crashed the second car midway through the session, his third key error in as many race weekends.
The teams were unable to do any running in the final minutes of the race because of Sainz's accident and a second red flag when Williams stopped on track.
Mercedes introduced their first significant upgrades of the season, which they started with a car that was close to a second off the pace.
The Briton was second fastest behind Leclerc in the first session as drivers had their first taste of the new Miami street track.
It's too early to say if this is indicative of permanent progress for Mercedes or if it's the result of a series of aspects particular to this weekend, but it was certainly the first sign that the team may be getting on top of the problems that have afflicted them this season.
A lower-drag rear wing and revised front wing have been added to the car.
The team hoped that the rear wing would raise the speed at which theporpoising problem would arise and it seems to have worked.
It is possible that circumstances have helped them.
The upgrade appears to have worked, but at the same time this is a lower-downforce track that might have helped their car's characteristics and the hot temperatures in Miami could have alleviated their problems with getting temperature into their tyres on a first flying lap.
Russell said that they don't really understand why they hit the ground running.
The conditions here would suit us better. This is the first real hot race of the season so for sure that has played a big factor in our struggles with tyre warm-up. It is only Friday. Not getting carried away.
It has definitely been a really productive day for us and the most productive Friday we have had.
Hamilton had a bad time. His car looked less stable out on the track and he was slower than Russell all day.
There are definitely positive elements from today. I am still having trouble with the car. George looked great but we are trying a lot of different things and hopefully improve.
The top 10 was completed by Alpha Tauri's Pierre Gasly, Alfa Romeo's Zhou Guanyu, Alpine's Esteban Ocon, and Kevin Magnussen.
The second Alfa Romeo of Valtteri Bottas did not take part in the session after a crash in the first hour of running.
Perez appeared to have a slight advantage over Leclerc and then Russell in the short race simulations that were completed at the end of the session.
Verstappen was late for the start of the session after overheating in the first, forcing Red Bull to change his gearbox.
When he went out on the track, his car had a mechanical problem and he had to tour slowly around the pits, which caused a rear brake disc to catch fire.
Verstappen said that this is an extremely painful day and that he only did four or five fast laps. We don't have any information on my car.
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