Global oil demand won’t stop growing before 2040 despite pledges made at the Paris climate change summit last year to cap greenhouse-gas emissions, the head of the International Energy Agency said.

IEA Executive Director Fatih Birol’s comments have added to a debate over when oil consumption—which has steadily grown for decades—will begin a sustained decline, a change known as peak demand. Royal Dutch Shell PLC’s Chief Financial Officer Simon Henry caused a stir earlier this month when he said the company believes demand for...