The prime minister said Gove, the Cabinet Office minister, would ask for the “best scientific, moral, philosophical, ethical viewpoints” before reaching a conclusion.
But speaking to broadcasters on Tuesday, the day after unveiling his roadmap for ending England’s lockdown, Johnson said there were “deep and complex” ethical issues involved in introducing domestic vaccine passports.
“We’ve never thought in terms of having something that you have to show to go to a pub or a theatre,” he said.
“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.”
He said when it came to foreign travel there was “no question” a lot of countries would demand proof people had received a Covid vaccine before being allowed entry.
“It’s going to come on the international stage whatever,” he said.
In December, Gove ruled out the introduction of vaccine passports. “I certainly am not planning to introduce any vaccine passports, and I don’t know anyone else in government who is,” he told Sky News.
Asked if there was a possibility they could be introduced, he added: “No.”
Johnson also said on Tuesday he was “very optimistic” that he will be able to ease all the restrictions by the June 21 target date.
But he said “nothing can be guaranteed” and warned the date could slip if people were not “prudent and continue to follow the guidance in each stage”.
“Some people will say that we’re going to be going too fast, some people will say we’re going too slow,” he added.
“I think the balance is right, I think it is a cautious but irreversible approach, which is exactly what people want to see.”
The relaxing of rules is heavily dependent on the progress of the vaccination programme.
Matt Hancock, the health secretary, told BBC Radio 4′s Today programme the government is working “incredibly hard” to ensure as many people as possible receive a jab.
“We want to see that vaccine uptake go as high as possible. But it’s absolutely on all of us to come forward and get the vaccine. It’s the right thing to do,” he said.