The British Olympic Association says it will not "endanger the health" of athletes by encouraging them to prepare for Tokyo 2020 if it is not safe to do so.
The International Olympic Committee remains fully committed to the Games starting on schedule on July 24.
However, athletes have raised concerns that current social distancing restrictions imposed due to the pandemic are making it impossible to prepare properly.
The BOA says it supports the IOC's ongoing decision-making process but added: "We can be categorically clear that we will not endanger the health and well-being of the athletes or wider delegation at any point.
"It is imperative to preserve competitive integrity for athletes, but it is clearly only wise for athletes to continue to prepare for the Games where it is safe and appropriate to do so, within relevant Government and public health guidelines."
Officials from the BOA and British sports federations returned from Tokyo this week following a series of venue and athletes' village visits, and reported that preparations appeared to be continuing as normal.
However four-time Olympic champion Sir Matthew Pinsent believes it is "folly" for the International Olympic Committee (IOC) to insist the Tokyo Games will go ahead.
"I think it's the IOC saying we must try and get through if we can, which I have a degree of sympathy with, it just runs counter to what every health authority and government is saying around the world," Pinsent told BBC Radio 4's Today programme.
"We've seen lockdowns across Europe and across Asia at different timescales but this is coming and the idea that the Olympics are going to carry on regardless I think is folly.
"On a global front we have other priorities and I think the Olympics should at the very least be saying we should postpone or indeed just cancel at this stage and we'll talk about postponement later on.
"I just don't think there's much of a choice at this stage. For much of the European countries as well Asian countries, organised sport in any meaningful way has ceased and that's from government advice.
"I don't see there's any way forward for an Olympic athlete to train effectively even as an individual but particularly in a team environment.
"I just think it's unfair actually, I think it's unfair almost for the Olympics to say we're going to carry on, the Olympics are still happening, we are committed to the Olympics in July, because there are two big forces in an Olympic athlete's life, which is the Olympics and everything else and those two things are pulling in different directions at this moment and it's very very difficult for them individually when they've got that tension in their own heads."
Pinsent believes the IOC should follow the lead of other sporting organisations which have suspended matches or tournaments in order to give themselves time to assess the long-term situation.
"If you had a decision tree, the first one is are the Olympics going to carry on in Tokyo in July as planned and to me that very soon is going to be a no, a firm no," the 49-year-old added.
"The decision whether to reinstate it in Tokyo, whether it's later in the year or next year or delay by two or four years, is a decision that does not have to happen now. That can take time."
World Athletics president Lord Coe admits that the Games could logistically be held in September and October, but believes a decision does not need to be taken now.
"That is possible, anything is possible at the moment," Coe, who was chairman of the London 2012 Games organiser Locog, told BBC Radio 4's Today programme.
"But I think the position that sport has certainly taken, and it was certainly the temperature of the room in the conversation I had the other day with the IOC and our other federations, is that nobody is saying we will be going to the Games come what may.
"And it may be that over the course of changing events, and they're changing by the hour, that that is something that we have to confront. But it isn't a decision that has to be made at this moment."
Asked if the Olympics could be delayed to 2021, Coe added: "That seems on the surface of it an easy proposition, but member federations actually avoid Olympic years often to have their world championships.
"Athletics has its world championships at exactly those dates that you're talking about in 2021 in the United States (August 6-15) so it's not quite as easy as just saying we'll move one down.
"The European football championships have moved to next year, that too would clash. The sporting calendar is a very complicated matrix, it's not that simple to just simply say we'll ease one event from one year to the next."