Boris Johnson on Tuesday confirmed he has tasked the Chancellor of the Duchy of Lancaster with overseeing an assessment of whether the controversial passports should be used.
Speaking at a school in south London, the Prime Minister suggested there was “a case for it”.
He said: “This is an area where we’re looking at a novelty for our country. We haven’t had stuff like this before, we’ve never thought in terms of having something that you have to show to go to a pub or a theatre.
“There are deep and complex issues that we need to explore, and ethical issues about what the role is for government in mandating or for people to have such a thing or indeed in banning from people doing such a thing.
“We can’t be discriminatory against people who for whatever reason people can’t have the vaccine. There might be medical reasons why people can’t have a vaccine.
“Or some people may generally refuse to have one, I think that’s mistaken. I think everybody should have a vaccine, but we need to thrash all this out.
“In the interval [during the rollout of the vaccines] what I want to see is a proper review into the issue.
“That’s going to be led by Michael Gove, the Chancellor of the Duchy of Lancaster, who will be getting the best scientific, moral, philosophical, ethical viewpoints on it and will work out a way forward.
“The fervent libertarians will reject, but other people will think there’s a case for it.”
Unveiling his roadmap on Monday, the Prime Minister had confirmed a study into vaccine and testing certificates will be one of four reviews conducted as he bids to ease restrictions.
It has been suggested that vaccine certificates or passports could open up the possibility of international travel, which is currently banned until at least May 17.
The use of Covid status certificates could allow venues to deny access to those that cannot provide evidence that they have either been vaccinated against coronavirus or tested negative for it.
Speaking on Tuesday, Mr Johnson claimed there was "no question" that for international travel a lot of countries would want vaccine passports.
He said: “They will be insisting on vaccine passports in the way that people used to insist on evidence that you'd been inoculated against yellow fever, or whatever.
"So it's going to come on the international stage, whatever.”
Earlier health secretary Matt Hancock had appeared to rule out the use of vaccine passports to access certain services.
Speaking to LBC Radio, he said: "There are some things where that might be OK, but there’s some areas where it definitely wouldn’t and so we’re going to have a review of that, consider all of those details, the ethics which is very, very important and challenging, and then come forward with a considered view."
Senior ministers had previously repeatedly dismissed the idea of introducing vaccine passports, with the UK Government’s vaccines minister Nadhim Zahawi brandishing them “discriminatory”.