Verstappen led team mate Sergio Perez one-two in the opening session and was again fastest in the late afternoon when last year's winner Carlos Sainz was second on the timesheets for Ferrari.
"I think it was quite a good day for us," said Verstappen. "It was quite slippery in the beginning but also I think that is due to the high pressures we are running on the tyres.
"Overall, the car has been performing really well. The performance has been strong in both sessions and we could complete our programme."
Albon was an eye-catching third in both sessions for a team currently ninth out of 10, with American rookie teammate Logan Sargeant also fifth in practice two.
Red Bull boss Christian Horner said the Williams pair had been "super impressive".
"They’re proper laps and not just one lap, their long runs look pretty sensible as well. Based on that pace they would be a factor in the group behind," he said.
Dutch double world champion Verstappen produced a best time of one minute 28.078 in practice two after lapping in 1:28.600 in the first. Sainz was just 0.022 slower.
Perez, Verstappen's closest title rival but a hefty 81 points behind after nine races, was 0.448 slower in session one and 0.264 down in the later one when the Mexican finished fourth.
Verstappen has won seven races this season and is chasing a sixth in a row for the first time in his career.
MCLAREN RECORD
Red Bull have won every race and, when last year's final is added to the tally, are chasing an 11th win in a row to equal the 1988 McLaren record set by Ayrton Senna and Alain Prost.
Aston Martin's Fernando Alonso was fourth and 10th respectively, with Ferrari's Charles Leclerc fifth in the opening one.
The Monegasque did not set a time later on as Ferrari worked to fix an electrical issue on his car.
Mercedes made a slow start to the weekend, with seven-time world champion Lewis Hamilton only 12th and teammate George Russell 14th in practice one, when they were the only ones not to use the soft tyres.
Russell was 12th and Hamilton, winner of his home race a record eight times, was 15th.
"It's a tough car to drive. No matter what we do to set-up, it continues to be a tough car to drive," said Hamilton.
"On a single lap I didn't feel any improvement between tyre compounds, which shows that something is wrong. We're missing something. On the long run it didn't seem to be too bad, so that's a positive at least."
Mercedes have a front wing upgrade but Hamilton reported bouncing halfway through the session while Russell said his car was "all over the place" at turns six and seven.
McLaren's Lando Norris was eighth and 14th fastest with Australian teammate Oscar Piastri 10th and ninth. Both had the latest upgrades on their cars after just Norris in Austria, where he finished fourth.
