Verstappen was second in practice but the pace of the Red Bull on longer runs appears to have an advantage over the Aston MartinFernando Alonso has rejected the idea that he could start the Bahrain Grand Prix from pole position despite setting the pace in Friday practice.
The Aston Martin driver was 0.169 seconds quicker than world champion Max Verstappen's Red Bull, whose team-mate Sergio Perez was third fastest.
Alonso said: "I am not thinking that high. I don't know exactly what position would be a good one for us."
The two-time champion also ruled out fighting for the world title in 2023.
Alonso, who has moved to Aston Martin for this season after two years with the Alpine team, was quick on both short, low-fuel runs and longer stints with race-level fuel loads on the first practice day at the season-opening race.
He was fastest of all on overall one-off lap times, and just 0.048secs on average slower than Verstappen - and faster than everyone else - on the race-simulation runs.
Alonso's performance, if repeated in qualifying and race, marks a dramatic step forward for Aston Martin, who finished seventh in the championship last season.
The 41-year-old two-time world champion - who has not won a race since the 2013 Spanish Grand Prix, when he was driving for Ferrari - said: "It is not the same fighting for 12th, 14th as for the top five, because the pressure and adrenaline is different. So there are a lot of things we as a team have to bring together in this process.
"I expect we will unfortunately make some mistakes. I may maybe make some mistakes. It is a completely new team, new procedures.
"We have to be with the feet on the ground. The target has to be fighting for the championship in the long term; I don't think this year."
He said that, after last week's pre-season testing session at Bahrain, Aston Martin knew they had made progress but that he was expecting to be fighting in the lower half of the top 10.
"After testing we were thinking to be in Q3 with both cars," he said, "score as many points as possible in the first couple of races and try not to make mistakes."
The Aston Martin was expected to have made a step forward but Alonso's performance was a surprise - even to the team themselves.
"It felt good," Alonso said. "Obviously it is good to see the times that we are competitive, after testing there is always mixed feelings as to where you are.
"At the moment, we are just concentrating on ourselves. There are still some things to improve on the car. The balance was not completely perfect and the team has to change quite a few things. We are trying to reinforce every area of the team and we try to regroup everything and be the strongest team possible."
Alonso joined Aston Martin this season after previous team Alpine only offered him a one-year contract extensionWhat about the rest of the field?
Ferrari's Charles Leclerc was fourth fastest and Lewis Hamilton the quickest Mercedes in eighth, 0.636secs off the pace.
Nico Hulkenberg's Haas, Lance Stroll's Aston Martin and Pierre Gasly's Alpine filled the gaps ahead of Hamilton.
McLaren's Lando Norris was ninth fastest ahead of the Alfa Romeo of Zhou Guanyu. Hamilton's team-mate George Russell was down in 13th and the second Ferrari of Carlos Sainz 14th after making an error on his fastest lap.
Leclerc was the fastest Ferrari driver on race pace, but nearly a second a lap slower than Verstappen, and the Mercedes drivers slower again, and also behind Gasly and and Norris.
The session was relatively incident-free. McLaren's rookie driver Oscar Piastri had a big lock-up when he saw Stroll's Aston Martin in front of him late at the first corner, and Alonso abandoned a race run on the medium tyre when he locked up entering Turn 10.
The soft tyre was the preferred tyre for all drivers on the race runs, suggesting it will be used by most for the start of the race.
