"There will be a lot of death unfortunately," Trump said, stating that the government was focussing on supporting the hardest hit regions.
The US has more than 300,000 cases of coronavirus and over 8,000 deaths due to COVID-19.
More than 3,500 deaths are in New York state which has become the epicentre of the country's outbreak.
Some global officials have criticised the US for buying up key medical supplies such as masks.
There have been some hopeful signs in Europe, where despite the somber death toll, Italy showed a decrease in the number of patients in intensive care.
Patients in ICUs in Italy dropped to just under 4,000, a decrease for the first time since the beginning of the crisis, the health ministry said.
The death toll also went down: at least 684 people died compared to over 700 the previous day, Italian national media reported.
The numbers show that the social distancing measures put in place in the country in early March could be having an effect.
In Spain, the daily number of new coronavirus cases dropped for a second day in a row - another piece of good news that suggests the rate of the outbreak has begun to lessen in the country.
More than 7,000 infections were recorded in the last 24 hours, according to latest figures from the Spanish Health Ministry.
This is less than the number of new cases reported in the last two consecutive days.
It comes as Spanish Prime Minister Pedro Sanchez extended the country's three-week lockdown to April 25, telling citizens: "We are in a position to bend the curve."
Speaking at a press conference on Saturday, he warned that an eventual return to normality would "not be easy" and that a new world awaited.
"If the climb has been hard, let's not fool ourselves, the descent will not be smoother," he said, adding: "We are facing the great crisis of our lives."
"The world that is coming, in which we are already, will not be like yesterday, but even less will be like the day before yesterday."
Spain's total number of COVID-19 infections now sits at 124,736, while more than 11,000 people have lost their lives.
It has now also overtaken Italy in its number of cases to become the second worst virus-hit country in the world - behind that of the US.
Any consideration of relaxing stringent lockdown measures during this time "would have a worse result than returning to the starting point," Sanchez said.
He added: "The victory that puts an end to it will only come with a vaccine that unfortunately will take a few months."
France's nursing homes hit hard by coronavirus
More than 2,000 people have died in nursing homes in France since the beginning of the coronavirus epidemic, a much higher figure than the partial numbers provided by the government earlier.
It brings brings to light the dire situation for elderly people who need long-term care and who had previously not been counted as part of the official death toll for the outbreak.
Spain's defence minister said last month that elderly people had been found abandoned in some nursing homes and that although "the vast majority" of nursing homes "are fulfilling the obligation" to care for their residents, others that are not.
In French hospitals, meanwhile, there are now more than 6,800 people in intensive care units, the French health ministry added, as cases continue to rise.
A Flourish chart
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