The winner of the last two Hungarian Grands Prix lapped the Hungaroring circuit outside Budapest with a best time of one minute 25.814 seconds in the morning and 1:24.482 in the afternoon.
Rosberg was second fastest in both, 0.183 and 0.238 slower than the 2008 champion in the sessions with track temperatures rising to a sweltering 55 degrees celsius after lunch.
Ferrari's Kimi Raikkonen and Fernando Alonso were the closest to the dominant duo, who have won nine out of 10 races so far between them, in the morning with third and fourth places respectively on the timesheets.
However Red Bull's quadruple champion Sebastian Vettel, who has never won in Hungary, was third fastest in the second practice with Alonso fourth.
Hamilton is 14 points adrift of Rosberg, despite having won five races to the German's four, but has a far better record in Hungary. The Briton has won four times there in total, a record he shares with Germany's now retired Michael Schumacher, whereas Rosberg has yet to stand on the Hungaroring podium.
Raikkonen also has a great record at the track, which counts almost as a home race for Finnish drivers, with victory for McLaren in 2005 and second place in the last two years with Lotus. The Finn needs a good result this weekend after being eclipsed by Alonso so far this season. Raikkonen is the only driver on the grid who has yet to beat his team mate this year.
The morning session opened with Max Chilton's Marussia on fire in the pits, with the flames quickly extinguished, after oil leaked onto the exhaust.
There was less drama in the second, other than a few harmless spins and slides.
Hamilton could be heard enquiring over the team radio, however, whether there was something wrong with his car's front brakes - a worrying sign after a front brake disc failure pitched him out of qualifying in Germany last weekend. The Briton had to battle back in that race from 20th on the grid to third, with Rosberg winning.