The R&A is continuing planned preparations for the AIG Women's British Open scheduled for 20-23 August alongside The Open Championship which is due to take place from 16-19 July.
Golf's governing body says it is undertaking a "comprehensive evaluation" of current plans to host the events at Royal Troon and Royal St George's and were considering "contingency options".
The Masters, USA PGA Championship and ANA Inspiration have already been postponed as a result of the global coronavirus pandemic with 11 European Tour events either cancelled or postponed.
The R&A released a statement explaining that their focus remained trying to ensure the competitions go ahead as planned but with the health and safety of participants and fans at the forefront of any decision.
"We are undertaking a comprehensive evaluation of our plans to stage The 149th Open at Royal St George's and the AIG Women's British Open at Royal Troon, which are four and five months away respectively.
"This includes examining a range of scenarios for staging the championships, with our focus on proceeding as planned, as well as considering other contingency options available to us."
The governing body has already been forced to cancel two international amateur events due to take place next month, the R&A Student Tour Series Final at St Andrew's and Carnoustie and The R&A Girls’ U16 Amateur Championship at Fulford.
Chief executive Martin Slumbers said his organisation would be monitoring the changing situation carefully and were conscious of their responsibilities.
"We have some time before we start building the infrastructure at both venues and so we are keeping the scheduled dates in place for The Open and AIG Women’s British Open at this point.
We recognise that this is a rapidly changing situation and we will keep everyone informed of any changes to our plans.
These are difficult times but we are bearing in mind our responsibility for what’s right for golf and most importantly for society."
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