Verstappen had started the race level on points with Hamilton but 9-8 ahead on wins, and there were fears a collision could settle the outcome.
The Dutch driver Jos Verstappen had asked the F1 team to decide on his future by a Friday deadline.
Factbox on Dutch driver Max Verstappen, who became Formula One's youngest race winner, aged 18, at the Spanish Grand Prix on Sunday.
Luca di Montezemolo's resignation as Ferrari chairman on Wednesday severs an historic link with the company's late founder Enzo and marks the end of an era for Formula One's most successful and glamorous team.
Dutch teenager Max Verstappen is a rare talent comparable to the late Ayrton Senna, according to Red Bull's Formula One consultant Helmut Marko.