"But it can also take years as there can of course be setbacks, as we have seen some with other vaccines," he said.
"The development of vaccines is one of the most challenging and difficult tasks in medicine."
Trump, relaunching his re-election campaign on Sunday, was more optimistic.
"We are very confident that we're going to have a vaccine at the end of the year, by the end of the year," he said in a Fox News "town hall" show broadcast from the Lincoln Memorial in Washington, DC.
"The doctors would say 'well, you shouldn't say that.' I'll say what I think," he said.