The head of the British Olympic Association (BOA) says the organisation is still "trying to convince" some athletes to have the Covid vaccine before Tokyo 2020 starts next month.
Chief executive Andy Anson said "well over 90%" of British athletes will have two vaccine doses by the Olympics.
But he also admitted "there are individuals who didn't want to be vaccinated".
"We're trying to convince them it's the right thing to do," he added.
"People have got the right to choose, and we have to respect that. But it's not necessarily that helpful."
In a wide-ranging and exclusive interview with The Sports Desk podcast, Anson said the BOA had been running a "mammoth programme of vaccination of the whole entourage, well over 1,000 people… because that will lessen the risk", but there had been challenges.
"There's been some difficulties with some athletes who have been travelling around the continent," he said. "I'm pretty sure that nearly everyone will have at least one dose. We'll keep trying right until the last minute."
Background
The Olympics were postponed for the first time in their history in 2020 as a result of the pandemic and are set to go ahead on 23 July, despite significant opposition from the public and medical experts in Japan.
Organisers insist they will be safe and secure, but the vaccination roll-out has been slow.
Coronavirus case numbers have been falling since May, when there were more than 6,000 a day across Japan, and a state of emergency in Tokyo has been lifted.
In the host city, experts have said the daily infection rate should be below 100 in order to hold the Games safely.
However, the city's health authorities reported 619 new infections on 23 June, and the average for the last seven days is 423 new cases a day.
The BOA is sending a team of more than 370 athletes to the event.
'Toughest environment in sports'
Rupert Wingfield-Hayes takes a look at how the athletes' village hopes to mitigate the risk of CovidAnson said the 18,000-bed athletes' village in Tokyo will be "probably the toughest environment in sports at this time".
"Eleven thousand athletes basically sharing one dining hall, that's the challenge.
"So we are putting in place very strict protocols along with [the organisers] to make sure, to the fullest extent possible, we follow the rules of isolation, distancing, and just keeping in our own 'semi bubbles'.
"We will eat together - we won't be mixing in the village like people normally would. So that's the tough bit. But we're confident that we've got enough people around from a medical perspective to make sure that environment is as safe as it possibly can be."
This week two Ugandan athletes tested positive after arriving in Japan despite being fully vaccinated.
When asked if he feared similar cases involving British athletes, Anson said: "I'd be a little naive if I said there weren't going to be.
"We've got to plan that there will be cases… we anticipate that and when there are cases, we manage them properly.
"But clearly there is that risk that people test positive.
"Being vaccinated gives you a chance to get out of any quarantine environments earlier.
"I think we all know that this pandemic is a very difficult thing to manage."
The 'fever clinic'
Athletes suspected of having Covid will be sent to the village's 'fever clinic', and could be moved to an 'isolation hotel' if a positive case is confirmed, ruling them out of their events.
"The athletes are very aware of the risks, because they've been competing and some have seen colleagues miss competition," said Anson.
"We have some brilliant people who are very focused on mental health and wellbeing. But it won't be easy if it happens."
Anson confirmed that Team GB athletes would not need to quarantine for six days on arrival in Japan after the UK was added to to Japan's travel 'red list' because of rising cases of the Delta variant.
"We got in contact with the IOC and said that would be completely unfair. And they acknowledged that straight away," he said.
"They came up with this plan for Team GB, where for three days after arrival we won't be able to train or mix with athletes from other nations. But that's fine, because the vast majority of our athletes are going to the preparation camp which is our own environment."
'Obsessing about Covid'
Despite the restrictions, Anson believes athletes will still be able to enjoy the Olympics.
"One of the messages that came to us very early on from the athletes was, 'please don't make this the Covid Games for us. We want to see this as the Olympic Games. It's our chance to shine.'
"So we as an organisation are obsessing about the impact of Covid. We're trying to take all of that weight off the athletes' shoulders so they can go out there and compete and enjoy it without worrying about all this other stuff. So I think they can be fun.
"There are some sad things - the fact the athletes have to leave the village within two days of competing and then come home means they won't be able to watch their fellow athletes.
"Friends and family were the one group we were trying to push back on to see if they would be allowed in the country. But the Japanese government, rightly probably, took the decision there were no international visitors.
"So that is a shame, but we will make it as positive an environment as possible."
'The right thing to do'
Despite fears the Games may trigger a surge in coronavirus infections, up to 10,000 Japanese fans will be permitted at venues.
"There's nothing bigger and better than the Olympics for uniting the whole world. Yes, it's going to be tough, and different," said Anson.
"But I'm absolutely convinced it's the right thing to do.
"It's got the chance to lift the whole country and actually the world, and it could be an amazing experience."
Anson admitted that cancellation of the Games would have meant a "very difficult situation for the BOA".
"And that would have been replicated all around the world, not just for national Olympic committees, but for international federations.
"It's not been about greed. It's been about the financial sustainability of the whole sporting landscape."