The Canadian delivered the upbeat prediction in a message to golf fans following the postponement of the Aberdeen Standard Investments Scottish Open, due to be held at The Renaissance Club in East Lothian in July.
In addition, two other events - the BMW International Open in Germany and the French Open - have both been cancelled due to the ongoing threat posed by COVID-19.
"Public health and well-being continues to be our absolute priority," said the Canadian. "That is why today we have announced the cancellation of the BMW International Open and the Open de France, as well as the postponement of the Aberdeen Standard Investments Scottish Open.
"These are three of our most prestigious events, but it is essential that we continue to follow the guidance of the individual national Governments as we stand united in our efforts to stop the spread of Coronavirus."
Tournaments have now been either postponed or cancelled until the end of July, but Pelley hinted that he is hopeful things can get up and running again with the British Masters, due to be hosted by Lee Westwood at Close House, near Newcastle.
"My primary message is actually one of optimism because I am genuinely hopeful that from now on the information I send in relation to our 2020 schedule will be positive," he added.
"We cannot emphatically commit to a start date because, as I have said many times, we will not resume until it is safe, and we are permitted to do so.
"We now have 14 weeks with no tournaments, but those three and a half months are also the time where the global situation may well begin to show signs of improvement. "There are already discussions centering around the easing of restrictions in several countries and everyone is optimistic that these can continue.
"This window also gives us the opportunity to continue working behind the scenes on a variety of scheduling options which would allow us to provide you with a busy calendar of golf to enjoy when we do resume.