6-8 minutos - Source: BBC
He had previously suggested that they could be relaxed as early as Easter, which falls in mid-April.
"The highest point of the death rate is likely to hit in two weeks," Mr Trump said.
He appeared to be referring to peak infection rates that experts fear could overwhelm hospitals.
White House medical adviser Dr Anthony Fauci had earlier warned that the virus could kill up to 200,000 Americans.
Dr Fauci said that it was "entirely conceivable" that millions of Americans could eventually be infected.
The US now has more than 140,000 confirmed cases.
As of Sunday evening, 2,493 deaths had been recorded in the country in relation to Covid-19, according to figures collated by Johns Hopkins University.
The US last week became the country with the most reported cases, ahead of Italy and China.
What did Trump say?Speaking during the latest Coronavirus Task Force press briefing at the White House on Sunday, the president said that measures such as social distancing were "the way you win", adding that the US "will be well on our way to recovery" by June.
Suggesting that the "peak" of death rates in the US was likely to hit in two weeks, Mr Trump said that "nothing would be worse than declaring victory before victory is won - that would be the greatest loss of all".
Analysts suggest that when Mr Trump referred to a peak in the "death rate", he probably meant the total number of recorded infections.
He said the decision to extend social distancing was made after he heard that "2.2 million people could have died if we didn't go through with all of this", adding that if the death toll could be restricted to less than 100,000 "we all together have done a very good job".
Mr Trump had previously said that Easter - 10-13 April - would be a "beautiful time" to be able to open at least some sections of the country. On Sunday he said that lifting restrictions at Easter was "just an aspiration".
"I wish we could have our old life back... but we're working very hard, that's all I know. I see things, I see numbers, they don't matter to me. What matters to me is that we have a victory over this thing as soon as possible," he said.
The president also talked on Sunday about the medical response. He said that "rapid testing" had been approved to get Covid-19 results within five minutes, and that doctors, nurses and other healthcare workers would be tested.
What's the situation in the US?Nationwide measures mean citizens must continue to avoid non-essential travel, going to work, and eating at restaurants or bars. Gatherings are limited to groups of under 10 people.
But stricter restrictions apply to millions in some of the worst-hit states.
On Saturday residents of New York, New Jersey and Connecticut were instructed not to travel elsewhere within the country for 14 days.
Non-essential gatherings in New York City are banned and most businesses are closed as the city faces more than 33,000 cases. Police can issue fines of $250-500 (£200-£400).
In California, a "shelter in place" order remains.
What about the shortage of equipment?Earlier on Sunday, Mr Trump accused hospitals in some states of "hoarding" ventilators, face masks and other critical medical supplies.
"We do have a problem with hoarding... including ventilators. Hospitals need to release them - in some cases they have too many, they have to release medical supplies and equipment," he said.
Hospitals "can't hold [ventilators] if they think there might be a problem weeks down the road", he said, alleging that some were "stocked up".
The availability of ventilators is a major concern among health professionals as demand has surged. A number of states have warned that they will soon not have enough to treat patients suffering from Covid-19.
The virus can cause severe respiratory issues as it attacks the lungs, and ventilators help to keep patients breathing.
What's the global picture?More than 33,000 people are now confirmed to have died worldwide after being infected with the new coronavirus.
Some of the latest major global developments include:
- In Germany the number of confirmed cases has jumped to over 57,000 - an increase of 4,751
- Australia has tightened its restrictions, with public gatherings now limited to just two people and playgrounds, outdoor gyms and parks closed from Monday
- South Korea's President Moon Jae-in has said emergency cash payments will be made to all households except the top 30% by income
- In the UK, Prime Minister Boris Johnson revealed that about 20,000 former NHS staff had returned to work to help the fight against coronavirus
- Spain recorded a new daily record of deaths, reporting 838 victims on Sunday
- Italy recorded 756 new deaths over 24 hours, bringing the total to 10,779 - a slight drop in the daily toll
- France reported 292 new deaths, bringing its total to 2,606 as specially modified trains began transporting patients from the worst-hit areas to hospitals in the south
- Tight new restrictions in the Russian capital Moscow allow residents to leave their homes only for medical emergencies, essential work and to shop for food or medicine
- The price of oil has sunk to levels not seen since 2002 as demand for crude collapses