In 2007, Alonso allegedly blocked Hamilton in the pits to prevent him from taking pole position in the Hungarian Grand Prix.
"I do not feel like I ever had a personal issue with Fernando," Hamilton said on Thursday night.
"I do not think we ever necessarily had an issue between us, except we were trying to beat each other and murder each other's laps on the track," the five-time world champion added.
Regarding Polish racing driver Robert Kubica's F1 comeback, Hamilton said he hoped "he works on his strength," adding "it is exciting for the sport to see him back in action."
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