Racing activity was suspended last month until the end of April before the government introduced lockdown measures.
The BHA said in a statement https://www.britishhorseracing.com/press_releases/bha-extends-suspension-of-racing that it had not set a new date for ending the suspension but plans were in place so that the sport was ready to resume as soon as is possible.
"The BHA has been working with trainers, racecourses and other participants to develop a phased plan for resumption which will allow the sport to transition back to its normal fixture list later in the year," it said.
"Our plans continue to allow for a resumption in May, if that's possible. We assume it would be behind closed doors only, at a point when the safety of participants can be assured and the pressure on the health service allows.
"Because of the very strong likelihood that restrictions on mass gatherings will continue, the BHA has decided that racing with crowds will not be possible until June at the earliest."
The BHA said tough biosecurity measures would be in place to keep any risks to a minimum once activities resume.
Reported cases of the new coronavirus crossed 2 million globally and more than 131,100 people have died, according to a Reuters tally as of 1400 GMT on Wednesday. (Reporting by Shrivathsa Sridhar in Bengaluru Editing by Toby Davis)