President Donald Trump has said federal coronavirus guidelines such as social distancing will be extended across the US until at least 30 April.
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 it is feared 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.
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 United States overtook both China and Italy last week in the number of reported cases.
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”.