On a scorching hot day at the Hockenheim circuit, with air temperatures touching 34 degrees Celsius and the track temperature reaching 58 degrees, the Mercedes men were again in a class of their own as they continued their battle for this year's drivers' world championship.
Hamilton, who cut Rosberg's championship lead to four points by winning the British Grand Prix two weeks ago when the German suffered his first retirement of the season, clocked a best lap of one minute 18.341 seconds. That put him 0.024 seconds ahead of Rosberg.
"The temperatures are so high that it was very difficult with the tyres, but we learned a lot in that session. As usual qualifying is going to be very important like it is at every circuit we go to."
Australian Daniel Ricciardo was third fastest in the leading Red Bull, once again proving he has the pace to deserve his place among the elite, ahead of Finn Kimi Raikkonen of Ferrari.
Danish rookie Jan Magnussen was fifth for the improving McLaren team ahead of Brazilian Felipe Massa, of Williams, Briton Jenson Button in the second McLaren and defending four-time champion Sebastian Vettel of Germany in the second Red Bull.
The session saw the conditions take their toll on some teams with Japanese Kamui Kobayashi of Caterham suffering a close encounter with danger when his car burst into flames.
He jumped clear as smoke poured from the rear of his car and then ran back with several marshals, armed with fire extinguishers, to extinguish the flames.
Earlier, in the morning session, Briton Susie Wolff, the first woman to take part in a Formula One weekend for 22 years, had impressed for Williams by finishing 15th in opening practice topped by Rosberg.
"It was tough at the beginning, but so nice to be out on track every lap, going quicker and getting more feel in the car. I'm just really happy to have completed a successful FP1 session.
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