Although the Briton finished nearly a second down on pacesetter Sebastian Vettel in second practice, he is convinced that McLaren will be stronger in the race.
Button was ninth quickest in the afternoon after finishing sixth in the morning session.
"I don't think the car that we had in Nurburgring would have been that great around here, so it's definitely a step forward, which is nice to see," said Button.
"It should help us in the next couple of races.
"It's a big gap, but I think in race pace we are going to be a little bit closer. The car feel reasonably good around here.
"I think we made a good step forward, but this is a very unusual circuit. Some cars work and some cars don't. We are reasonably good."
Although he said earlier that he was not ruling out a victory this year, Button admitted McLaren was still far from the frontrunning teams.
"I don't know where we are compared to other people but the work that we are doing is positive. But there's still a long way to the front," he said.
Team-mate Sergio Perez was also upbeat about McLaren's progress, and the Mexican reckons he can make the top 10 in Sunday's qualifying.
"I think we did a good step. I'm not fully happy with the balance of the car, but I think we have a good potential to be in Q3 tomorrow," Perez said.