Having returned to Budapest to carry out duties on Wednesday, Raikkonen was also running the hypersofts in the final 15 minutes of testing and registered a 1:15.649.
The Pole's lap time of 1:18.451 was three tenths faster than McLaren driver Lando Norris. Raikkonen was less than 0.1s adrift; his 1m15.649s actually 0.001s slower than Antonio Giovinazzi managed in the Ferrari on the opening day, but the Finn was typically dismissive of the standings.
While Daniel Ricciardo took part on Tuesday, it was simulator driver Jake Dennis who got another run in the Red Bull, having made his debut during the in-season test in Barcelona.
Toro Rosso was the only team running a 2nd vehicle as part of Pirelli's tire testing schedule for Y 2019.
Having moved from the Pirelli test auto to the official Toro Rosso entry, Sean Gelael bounced back from his Tuesday mishap to go fourth fastest by the time the teams broke for lunch. The Italian completed 120 laps with a best time of 1:17.558, almost 0.6s quicker than Marcus Ericsson managed for Sauber on day one on the same hypersoft tyre.
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Nikita Mazepin took the undesirable honour of causing red flags either side of lunch, but shot up to fifth with a flying lap on hypersofts right at the end of the day.
After stopping midway through the first session, the GP3 race victor finally emerged an hour and a half into the afternoon's running.
Mazepin stopped at Turn 11 in the morning with a brake-by-wire issue that confined him to the garage for the rest of that part of the session, and hadn't added a huge amount of mileage in the afternoon when the Force India again stopped, this time at the penultimate corner.
Norris was the first driver to set a lap time as he continued his testing commitments into a second day, with his eventual best coming with his vehicle plastered with flo-vis paint.
After Kubica's run a year ago, Renault was again providing a significant opportunity in a current vehicle as Artem Markelov made his debut in a 2018 chassis. Brendon Hartley completed the team's normal test program while F2 driver Sean Gelael drove the Pirelli test vehicle with prototype tires fitted.