The BHA said it would make a decision on Monday as to when racing can resume, adding that it was "already planning for a variety of scenarios under which racing may recommence", including rescheduling meetings and races that have been cancelled.
"If you're to ask me again about Cheltenham I hope to be completely definitive then".
All racing has been cancelled in the United Kingdom on Thursday after one stable returned three confirmed Equine Influenza positives from vaccinated horses.
Officials are now facing millions of pounds in lost revenue in what could become the biggest shutdown in British horse racing since the 2001 foot and mouth epidemic.
One of the horses, Raise A Spark, ran at Ayr races on Wednesday and had shown no symptoms of the highly contagious virus beforehand.
He revealed he had been concerned about the health of a few of his string for a "couple of days" and his prompt action was praised by the BHA.
"In all previous form where infectious diseases have broken out in horse racing, either here or in other countries around the world, we learn from it each time and the key thing to do is to inform people to stop the movement of horses".
Thousands more swabs are expected to be received and tested over the coming days, the BHA added.
"We've got to get a hold of the situation swiftly - if we play Russian roulette with the evidence we've got we could have a problem for three to six months and no-one would thank us for that".
"This is a serious form of flu, which debilitates horses".
Responding to the news, Newbury's chief executive Julian Thick said: "We're clearly disappointed, it's a major race meeting for us, but horse welfare comes first".
A statement by Cheltenham read: "We are in contact with the British Horseracing Authority on this matter, who are handling it on behalf of British racing and providing regular updates".
"The full extent of potential exposure is unknown and we are working quickly to understand as much as we can to assist our decision making".
Personally I believe the BHA have acted quickly and diligently handling the affair swiftly.
'Losing something as huge as the Cheltenham Festival has a huge impact on the sport.
Equine influenza is not markedly different from human flu - infected horses suffer with coughing and runny noses and generally feel run-down.
North/South racing and transport of horses is unaffected.
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