"The U.S. will reach a horrific point in terms of death," Trump said, while voicing his optimism that "it will be a point where things will start changing for the better."
The president said that some 1.6 million people in the country have been tested for COVID-19 and received results.
The number of confirmed COVID-19 cases in the United States reached 337,620 as of midnight on Sunday local time (0400 GMT on Monday), with 9,643 deaths, according to the Center for Systems Science and Engineering at Johns Hopkins University.
Trump, who made the remarks during the White House Coronavirus Task Force news briefing, also said that by Tuesday, 3,000 military and public health workers will be deployed across the nation to cope with the pandemic.
The federal government will be sending some 600,000 N95 respirators Monday to New York State, the national epicenter of the coronavirus outbreak.
Meanwhile, the country is stepping up the development of treatments for COVID-19 patients, including experimenting with anti-malarial drug hydroxychloroquine and blood-related therapies.
At the same briefing, U.S. Vice President Mike Pence said hydroxychloroquine will be used in a trial covering 3,000 patients at a hospital in Detroit, Michigan, and the results will be tracked in a formal study.
Last week, Trump said hydroxychloroquine was being administered to 1,100 patients in New York along with Z-Pak, or azithromycin.
Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, told the White House briefing on Saturday there was no "definitive information to be able to make any comment" on whether the drug can be used to treat coronavirus.
In New York State, Governor Andrew Cuomo said that a decline in coronavirus-related deaths has occurred in the state, which could mean that the apex is almost here or it may be just "a blip."
The hardest-hit state has reported over 123,000 cases, outnumbering the total cases in Germany. Over 4,000 deaths occurred, with over 3,000 in New York City.
New York Mayor Bill de Blasio said Sunday that the city's medical supplies could make it through the middle of the week, which is better than expected.
"We thought as early as tonight there was the possibility of running out of crucial equipment like ventilators," said the mayor. "We have bought a few more days here. We believe now we can get to Tuesday or Wednesday with the supplies that we have."
The city will need 1,000 to 1,500 more ventilators for the rest of the week, he said, adding that an additional 45,000 medical personnel of every variety are also needed to fight the pandemic.