The 19-year-old Italian, winner of five races in a row until he retired in Spain this month and Ferrari's Lewis Hamilton ended the dominant streak, was 0.040 quicker than teammate George Russell in session one and then 0.237 faster than McLaren's Oscar Piastri in the second.
Piastri was consistently quick, third in a scorching first practice session with conditions declared a heat hazard, but Russell dropped to sixth at the end of the day after a disrupted second practice.
Red Bull's four-times world champion Max Verstappen was fourth in both practices for his team's home race, with Hamilton also fifth in both.
McLaren's world champion Lando Norris, last year's winner at the Red Bull Ring, was seventh in the early session but third in the later afternoon when McLaren looked to be Mercedes' closest challengers.
Issues for McLaren and Red Bull
Red Bull had a difficult start to the day with Verstappen suffering issues with his upgraded car, while teammate Isack Hadjar's car needed a hurried engine change and he missed the first 35 minutes.
Four-time world champion Verstappen complained that "the whole car is shaking under braking".
"At first we had an engine issue on Isack's car before the beginning of the session, so we had to do a very late call to change his engine," said team boss Laurent Mekies.
"And then on Max, we also had a troubled start with a couple of software issues that got us stuck in the garage."
Norris remained in the garage for the first 45 minutes as McLaren wrestled with a hydraulics problem while Piastri complained about his car's brakes.
Ferrari had F2 driver Dino Beganovic in Charles Leclerc's car for the opening session, clocking the ninth-best time, with the Monegasque returning for the later hour and going eighth fastest.
Sergio Perez's Cadillac brought out red flags with just over a minute remaining after the Mexican stopped on the uphill climb, with the session then ended prematurely and no drivers able to do any practice starts.
The Cadillac of Valtteri Bottas caught fire in session two after limping back to the pits with a damaged suspension and the car's floor sparking off the asphalt.
Japanese driver Ryo Hirakawa replaced Esteban Ocon at Haas for the session and knocked over one of the team mechanics when he overshot his pit box, fortunately without injury.