Verstappen shot up the grid on fresher tyres and chased down Leclerc, who was at the front, and overtook him with just three laps to go in Austria.
The pair had a battle at the next race at Silverstone and Verstappen, who has won two races this season so far, believes Leclerc was a "bit upset" following the thrilling race.
"Silverstone was a bit frustrating because I was stuck," Verstappen said to BBC Sport. "We were a lot faster than Ferrari. After Austria I think he was still a bit upset."
"For sure. He was racing very hard. I am fine with racing hard. But you could see in the way he was defending there was still a bit of anger from losing that victory in Austria - and that's fine. That's a normal reaction.
"But that's why it was also from my side frustrating because I didn't want to risk it too much. At the time, I was still thinking about maximising points. [I was thinking:] 'We are going to get there. Upgrades are coming. At one point, we are going to fight Mercedes.'
"So I was not going to go: 'Now I have to go, I have to out-brake him and there is a possibility we touch.'
"From my side, when I was behind him, it looked like he didn't care if we would have crashed at that time. My mentality was a bit different.
"But it's good. We had a bit of wheel banging. I am all for that. It's exciting. Of course, keep it in a controlled way. If you go 300km/h and you touch, it can be very dangerous. It was in that way enjoyable."