At a White House briefing today, however, Trump was more focused on mitigating damage to the US economy.
"We cannot let the cure be worse than the problem itself," he said, echoing a tweet he posted in all caps last night.
So far, 43,449 people have been infected in the US, and 545 people have died. The rise in cases is accelerating - today almost 10,000 new infections were identified and more than 100 deaths were recorded.
The President told Americans they would get through the challenge presented by the virus.
"The hardship will end. It will end soon. Normal life will return and our economy will rebound very, very strongly," Trump said.
"Our public health experts, who are terrific, are studying the variation in the disease across the country, and we will be using data to recommend new protocols to allow local economies to cautiously resume their activity at the appropriate time.
"We also have a large team working on what the next steps will be once the medical community gives a region the okay – meaning the okay to get going, to get back, let's go to work.
"Our country wasn't built to be shut down. This is not a country that was built for this. It was not build to be shut down.
"America will again, and soon, be open for business. Very soon. A lot sooner than the three or four months that somebody was suggesting. A lot sooner.
"We're not going to let the cure be worse than the problem."
The US is about halfway through a 15-day period of social distancing.
"At the end of the 15-day period, we'll make a decision as to which way we want to go, where we want to go, the timing – essentially we're referring to the timing of the opening. Essentially the opening of our country," said Trump.
After a short interlude, during which he promised that "vaccines are coming along very quickly" and urged Republicans and Democrats to make a deal on stimulus measures, the President returned to the subject of the economy.
"We are going to save American workers and we're going to save them quickly. And we're going to save our great American companies, both small and large," he said.
"This was a medical problem. We are not going to let it turn into a long-lasting financial problem. It started out as a purely medical problem and it's not going to go beyond that. We're just not going to allow that to happen.
"Our country was at our strongest financial point. We've never had an economy like we had just a few weeks ago, and then it got hit with something that nobody could have ever thought possible. And we are fixing it. We're fixing it quickly.
"Our country will be stronger than ever before, and we fully anticipate that, and it won't be that long."
One person notably absent from the briefing was Dr Anthony Fauci, who has previously been the face of the Trump Administration's coronavirus response.
At one point, Guardian reporter David Smith asked Trump whether Fauci agreed with him about the need to reopen the economy.
"He doesn't not agree," Trump replied.
"He understands there's a tremendous cost to our country."
CNN's Kaitlan Collins asked whether any of the medical experts advising the President had endorsed a quick easing of measures. He acknowledged they had not.
"If it were upt to the doctors, they'd say shut down the entire world for a couple of years," said Trump.
The President compared the US favourably to other countries, saying its coronavirus figures were "amazing".
"If you look at other countries, what they've been through, and look at the numbers. Compare them to ours, which is a much larger country than most, the numbers are pretty amazing," he said.
The US currently has the third-highest number of confirmed cases in the world, even though testing there was very limited until last week. Since testing became more widespread, its figures have been rising more sharply than any other country's.
Trump repeatedly compared the coronavirus to the flu, saying tens of thousands of people die from that disease every year but the economy does not shut down to stop it.
"We have a very active flu season, more active than most. It's looking like it's heading to 50,000 or more deaths — deaths, not cases. 50,000 deaths — which is, that's a lot," he said.
"You look at automobile accidents, which are far greater than any numbers we're talking about. That doesn't mean we're going to tell everybody no more driving of cars. So we have to do things to get our country open."
Another reporter asked what Trump would do if his medical advisers told him not to lift restrictions when the 15-day period expires next week.
"We can do two things at one time," he replied, suggesting the economy could function normally and the virus could be contained simultaneously.
"Parts of our country are very lightly affected. Very small numbers."
On a different subject, Trump highlighted his efforts to make the anti-malaria drug chloroquine available, once again suggesting it could be effective in treating the coronavirus. Some very early research has suggested it might be useful, but it remains largely untested.
Today a man in Arizona died after ingesting the drug in an attempt to stop himself from becoming infected. His wife, who also took it, is in critical care.
"The one that I'm very excited about is one we just mentioned. I think there's a real chance. We don't know. There's a real chance that it could have a tremendous impact. It would be a gift from god if that worked," said Trump.
"I think a lot of people are going to be, hopefully, they'll be very happy with the result. We're all going to be watching closely.
"It's been very successful with malaria. Very successful. Countries with malaria have had an interesting thing happen. They take this particular drug, it's a very powerful drug. There's very little semblance of the virus in those countries.
"There are those that say, because this drug is very prevalent because of the malaria. We'll see what happens."
The countries in question are located in Africa, which has indeed reported relatively few cases of the virus. But that may be due to its low level of testing.
At the start of last month, only two countries on the continent were even capable of testing, but the World Health Organisation has since helped dozens more get started.
