The president said at least 10 US companies were now making the medical devices, and some might be exported.
The virus can cause severe respiratory issues, and ventilators help keep patients breathing.
However, several state and local officials have warned hospitals are at risk of running out of equipment.
Governor Phil Murphy of New Jersey, the US state with the second-highest number of cases, was the latest to raise the alarm, saying the “need [was] dire”.
The US has more than 163,000 confirmed virus cases and over 3,000 deaths. On Monday, officials announced 540 new deaths in a 24-hour period, the deadliest day yet in the country.
New York City is the worst-hit place in the US, with 914 confirmed fatalities, according to Johns Hopkins University. The US last week became the country with the most reported cases, ahead of Italy and China.
Speaking at Monday’s Coronavirus Task Force briefing at the White House, Mr Trump said: “We have now 10 companies at least making the ventilators, and we say go ahead because, honestly, other countries – they’ll never be able to do it.”
Asked whether there would be enough ventilators for all patients in the US who needed them during a predicted peak in infections in two weeks’ time, Mr Trump responded: “I think we’re going to be in a very good shape.”
He said more than a million Americans had been tested for the virus, “more than any other country by far. Not even close”.
He accused a reporter who pointed out that South Korea had tested proportionally more people when measured by population size of negativity. He added that he should be congratulated on his administration’s progress in fighting the virus.