Norris lapped the Hungaroring, where track temperatures soared to 41 degrees Celsius, with a best time of one minute and 17.788 seconds on the soft tyres.
Verstappen, 84 points ahead of the Briton in the championship after winning seven of 12 races, was 0.243 off the pace in an upgraded car.
Ferrari's Carlos Sainz, fastest in the first session, was third quickest ahead of Red Bull's Sergio Perez and Mercedes' George Russell, whose team have won the past two races.
Leclerc brought out red flags to halt the session, with 43 minutes remaining, when he spun at speed and across the track and into the metal Armco barriers hidden behind advertising boards.
The medical car was deployed but Leclerc appeared unhurt and returned to the pits as a passenger. The session resumed 15 minutes later.
"When I lost it I thought the damage would be much bigger, it's not that big but obviously it's enough for us to not continue the session," Leclerc told reporters.
"It was my mistake but now its all about bouncing back tomorrow.
"The car was pretty good, the feeling is getting a little bit better, we had more of a consistent day compared to the last three or four weekends so that's positive".
Perez fourth
Red Bull boss Christian Horner said it had been a positive day for his team and probably under-performing Perez's best Friday since China in April.
"There’s a slight difference between the cars, both of them have upgrades and the only bit Checo (Perez) is missing is the engine cover and sidepod element," he told Sky Sports television.
"The floor, the wing and the rest of it is the same. We’ve got some great data."
Kevin Magnussen, out of a drive with Haas at the end of the season, was a strong sixth and seven times world champion Lewis Hamilton seventh for Mercedes.
"Today wasn't our best day of the season so far. The car set-up didn't feel great, and we weren't on our best form," said Hamilton, who won the previous British round at Silverstone.
"Whilst our single lap pace wasn't the best, our long run was decent. We are still a step behind the ultimate pace at the front but will do what we can to close as much of that gap as possible for Saturday."
RB's Daniel Ricciardo, Williams' Alex Albon and Aston Martin's Fernando Alonso completed the top 10.
Sainz had raised Ferrari hopes by leading triple champion Verstappen in FP1 (practice one), with Leclerc third, in a time of 1:18.713.
That time was 0.276 quicker than Verstappen.
Russell was fourth in FP1 ahead of Guanyu Zhou in the surprisingly quick and upgraded Sauber and the McLarens of Norris and Oscar Piastri.
Ferrari reserve Oliver Bearman, the Briton who will race for Haas next season, replaced Nico Hulkenberg at the US-owned team for the first session and was last overall.
Mercedes, sponsored by cybersecurity company CrowdStrike, reported minimal disruption from a global technical outage triggered by a software update.
"There was a bit of work that we had to do. We've got a lot of computers around the garage and in pit walls and things here, and those all needed updating, but we've worked through that," said Mercedes trackside engineering director.
