The foreign secretary told BBC1’s Andrew Marr Show that blanket vaccination could be completed earlier if the capacity is available to do so.
But government sources said that reports of a private target of the end of June to get a jab to all under-18s were “speculative”.
The government has previously committed only to offering a first dose of vaccine by mid-February to all over-70s, elderly care home residents, health and care workers and people with serious underlying health conditions.
But Mr Raab told Marr: “The plan is to get the first 15 million most vulnerable people vaccinated with the first dose by the middle of February.
“We then want to get by early spring another 17 million. At that point we’ll have 99% of those most at risk of dying of coronavirus administered with a vaccine.
“The entire adult population we want to have been offered a first jab by September.
“That’s the roadmap. We think we got the capacity to deliver it.
“Obviously if it can be done more swiftly than that, then that’s a bonus. The number one thing right now is to protect that roadmap and rollout and protect the NHS, given the new variants that we’ve seen.”