Boris Johnson said he is “very optimistic” Covid restrictions in England can be lifted on 21 June, but warned “nothing can be guaranteed”.
He said his roadmap for easing lockdown measures, laid out on Monday, was “a cautious but irreversible approach”.
The government will carry out a review into the idea of Covid status certificates or vaccine passports.
Speaking on a visit to a London school, he said there were “deep and complex and ethical issues” to consider.
Cabinet Office Minister Michael Gove will lead the review.
Earlier Health Secretary Matt Hancock said everyone “has to play their part” in leaving coronavirus rules.
Mr Johnson said the idea of vaccine certificates were a “novelty” for this country, saying that they had never before thought in terms of having to show something to go to a pub or the theatre.
In turn this meant that there were “ethical issues about what the role is for government in mandating… or banning people from doing such a thing.
“We can’t be discriminatory against people who can’t have the vaccine, there might be a medical reason, or some people may genuinely refuse to have one – I think that’s a mistake. “
But the prime minister said there was time to consider the issue at the same time as the vaccine rollout continued.