Rosberg set his fastest time of one minute 15.517 seconds in the opening 90-minute session, but stayed at the top with a slightly slower lap in the afternoon.
"In general our car was working well out there today," said Rosberg.
"Saying that, in Hungary we were very quick on Friday but then on Saturday and Sunday everyone was very close.
"It's a good start but we'll see more tomorrow."
Team mate and world championship leader Lewis Hamilton was second in both sessions on a dominant day for Mercedes.
Rosberg, however, seemed to have the measure of him and was comfortably faster in both sessions, although the champion was not perturbed.
"It's been a very chilled Friday," said Hamilton.
"No real surprises and a good first step for the weekend."
Rosberg heads into Sunday’s race at the 4.5-km Hockenheim track trailing Hamilton by six points in the standings, having ceded the overall lead to the Briton at the last race in Hungary.
Sebastian Vettel, making his first appearance on home soil in Ferrari colours, finished both sessions in third.
The four-times world champion, whose team announced a split with highly-regarded technical director James Allison on Wednesday, closed the gap to the Mercedes drivers in the afternoon but was still 0.594 seconds adrift of Rosberg.
Max Verstappen ended the day fourth ahead of Red Bull team mate Daniel Ricciardo, as both leapfrogged Ferrari's Kimi Raikkonen in the afternoon session.
Force India pair Nico Hulkenberg and Sergio Perez were seventh and ninth respectively with McLaren's Jenson Button in eighth.
The Briton was later taken to hospital for a "precautionary check-up" after complaining of eye irritation, his team said on Twitter.
Fernando Alonso, celebrating his 35th birthday completed the top ten.
Rosberg won the last race at Hockenheim in 2014 and a repeat would put the brakes on Hamilton, who has triumphed in five of the last six races.
It would also hand him a crucial psychological edge over the reigning champion heading into Formula One’s annual summer break.
(Editing by Toby Davis)
