Watch Dominic Raab's full interview with ITV News Political Editor Robert Peston
The foreign secretary also admitted the UK government made mistakes in the handling of the coronavirus pandemic and did not deny that there may be a delay to the June 21 unlocking.
Asked about claims that Mr Raab appeared a bit sceptical about taking the knee, after Prime Minister Boris Johnson told fans to "cheer, not boo" England players, he said: "My point has always been to respect the rights of people to express themselves."
Prompted further about whether supporters should be booing, he said: "I don't think you should ever boo your team, I think you get behind your team, particularly at a European championship."
Football fans should be supporting their team taking the knee, foreign secretary Dominic Raab said
England players taking the knee in protest against racial injustice before two friendly matches in Middlesbrough were met with boos from a section of the home crowd.
The Prime Minister’s official spokesman earlier this week declined to condemn those who booed players, only going so far as urging them to be “respectful”.
But Downing Street has now gone further to tell crowds not to jeer the national team after coming under pressure to take a firmer stance.
Asked about criticism that the UK did not start mass Covid testing early enough, Mr Raab pointed out that there would be an inquiry and said: "I don't think we need to be overly defensive. We know mistakes have been made.
"It is the first major pandemic. We're not like some of the east Asian countries that had SARS and other pandemics. We hold our hands up."
When questioned whether there would be a two or four week delay to the June 21 reopening, Mr Raab said with a smile: "You'll have to wait for Monday for that one."
Will there be a two or four week delay to the June 21 reopening? Dominic Raab answers the question
Clarifying Mr Johnson's comment that he wanted world leaders to focus on "building back more equal. Maybe in a more gender neutral, a more feminine, way", he suggested that the prime minister wanted to tackle women's issues.
He said: "If you look at everything from climate change and the ability to build back greener and we have a whole agenda on that, in particular targets to get international climate finance up, to getting girls back into education, I think we've learnt a lot about where the economic as well as the health damage is."
He also said the UK wanted to work together with other countries to tackle the pandemic.
He said: "We want even more multilateral coordination, so rapid response on pandemics, whether it is on surveillance or the ability to get vaccines and therapeutics licensed and on tap at pace. Keeping supply chains open."
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He highlighted the extra 100 million Covid-19 vaccines to be donated to other countries and the UK's proposals on climate change.
He said: "I think you're seeing a strong multilateral push and a sense that we cannot deal with a whole range of problems the world is facing unless we do it together."
Speaking about fears that there is a shortage of the Pfizer vaccine, he said: "We have got the supply chains and the security of supply to make sure we can deliver the targets.
"The question is just how quickly we can beat the variants to get those people who've had their first dose to get their second dose.
"We are confident in the arrangements we've got in place, and we always started with a wide range and a large stock of doses precisely to deal with every eventuality.