Formula One boss Bernie Ecclestone also played down the threat of a boycott over tire safety concerns and said the race would go on as scheduled on Sunday.
Three-time champion Vettel is seeking his first win on home soil and beat Rosberg by .235 seconds in the second practice, after finishing eighth in the slower morning session.
Vettel, a vice-president of the drivers' association that warned F1 of a pull out if tire problems experienced at the British GP last week persisted, sought to clarify the drivers' position.
"The general agreement was that we're happy Pirelli bought a new specification of tire for this event and want to thank them for their flexibility and reaction times — they were able to find a solution in only a couple of days," Vettel said.
"The circumstances that we raced under in Silverstone were not what we can accept, but I don't think we will see those issues again."
Vettel's fastest lap was 1 minute, 30.416 seconds. Mark Webber in the second Red Bull was third and Romain Grosjean fourth, ahead of Lotus teammate Kimi Raikkonen. Next was Ferrari's Fernando Alonso, who failed to complete a full lap in the morning because of electrical problems.
"Pirelli have done what they can and gone back to tires they know work here," Webber said. "It's impossible to tell how they will affect the performance of the car, but it feels comfortable so far."
Lewis Hamilton, who topped the morning session ahead of Rosberg, dropped to eighth in the afternoon.
Ecclestone, who came to Germany despite facing possible bribery charges in a Munich case, said the drivers were right in stating that it was their neck on the line.
But he told the German newspaper Die Welt the drivers understood that Pirelli would do everything to resolve the tire issue, which turned serious when five cars endured blowouts at the British GP.
"There is a big difference between thinking about something and carrying it out. If the drivers boycott the race, they risk losing their super licenses," Ecclestone said. "Such a boycott would serve no one and won't solve the problem faster."
There were no punctures in the practices, although some drivers complained about the quick degradation of soft tires.
Pirelli has asked teams to stick to operating requirements, backed by the International Automobile Federation.
Pirelli wants all teams to keep the tires within prescribed pressure limits and to stop switching tires from left to right and vice versa. The company also put Kevlar belts on the tires instead of the steel ones to reduce the risk of punctures.
Pirelli motorsport director Paul Hembery said it underestimated the problems caused by switching left and right rear tires, a practice widely used by teams until now.
"We got that wrong," Hembery told a news conference on Friday, adding that Pirelli had manufactured about 1,000 tires with new specifications over 48 hours.
"We wouldn't be racing if we didn't think they were safe," he said.
Rosberg, who won in Silverstone and took the checkered flag in two of the last three races, said he was pleased with his performance.
"It was an interesting day for us as we had to adapt to the new tires," he said. "They are different and require a different set-up, so today was a good opportunity to learn something. We want to understand them quicker and better than the other teams. Generally it seems that we are quick again over one lap and the long run was not bad."
Mercedes has held five of the last six poles, but has struggled to sustain the challenge in a race.
Former champion Hamilton is still seeking his first win since joining Mercedes this season.
"This morning went pretty well and the car felt good, but then we made some changes which didn't quite work out for us this afternoon. The car felt a little off balance," Hamilton said.Suggest a correction