Michael Gove has been tasked with leading a review into the possible use of vaccine passports as part of the roadmap for releasing England's coronavirus lockdown.
Boris Johnson announced that the Cabinet Office minister would head up the review as the Prime Minister acknowledged the "deep and complex issues" surrounding the introduction of Covid-19 status certificates.
Senior officials, including the Government's vaccines minister, Nadhim Zahawi, have frequently appeared to dismiss the idea of introducing vaccine passports in the UK.
But announcing his roadmap on Monday, Mr Johnson confirmed that a study into the use of vaccine and testing certificates will be one of four reviews conducted as part of easing the current restrictions.
Speaking at a school in south London on Tuesday, the Prime Minister told reporters that the introduction of such certificates should not discriminate against those who opt out of receiving the jab.
He said: "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 can't have the vaccine. There might be medical reasons why people can't have a vaccine.
"Or some people may genuinely refuse to have one. I think that's mistaken, I think everybody should have a vaccine, but we need to thrash all this out."
It is understood that the Government review will look at the possibility of the NHS coronavirus app featuring a digital health passport, which would carry details of vaccinations and negative test results.
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Proof of a recent negative coronavirus test or having been vaccinated could then be used to attend a particular event if required by organisers.
It is understood that combining the two is one option being considered by ministers, so as to avoid appearing to discriminate against those who decline the jab for health or moral reasons.
While the rollout of the vaccination programme continues across the UK, Mr Johnson said he wants to see a "proper review" into the issue.
He said: "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."
The findings of the vaccine passport probe are hoped to be available before stage four of the lockdown easing on June 21 is reached, the earliest date by which ministers hope all restrictions can be lifted.
Meanwhile, the UK will use its presidency of the G7 to seek an international approach on the use of vaccine passports as part of the effort to restart global travel.
A Number 10 spokesman said: "It's going to need an international consensus to be built on how to allow for greater foreign travel, and that's why we're going to try and do that via the G7, and through other sort of multilateral discussions, because ... it will be for different countries to determine their own regimes in relation to the quarantine and who they want to allow in, and we want to try and work together to get some sort of international framework."
The roadmap states that vaccinations could offer a route to the "safe and sustainable return" of international travel but any system must not disadvantage people who have not been offered or cannot access a vaccine.
