Anthony Fauci, head of the National Institute of Allergy and Infectious Diseases, echoed many governors in saying that health officials must first be able to test for the virus quickly, isolate new cases and track down new infections before social-distancing restrictions can be eased safely.
Trump's administration has recommended stay-at-home guidelines through the end of April, and the president has floated May 1 as a possible date to start reopening shuttered workplaces in some areas.
That date may be "a bit overly optimistic," Fauci, who has become a trusted national figure during the pandemic, said in an interview with the Associated Press.
"We have to have something in place that is efficient and that we can rely on, and we're not there yet," Fauci added.
Fauci, who frequently appears with Trump at White House coronavirus briefings, has previously contradicted Trump on some issues, such as an unproven medical treatment promoted by the president. Trump on Sunday retweeted a message on Twitter from a conservative political figure calling for Fauci's firing, but the president later denied plans to dismiss his adviser.
Trump, a Republican who before the pandemic had touted a vibrant US economy as a pillar of his Nov. 3 re-election bid, lashed out at Democratic state governors, suggesting they were "mutineers," after New York's Andrew Cuomo said he would refuse any order by the president to reopen the economy too soon.
"If he ordered me to reopen in a way that would endanger the public health of the people of my state, I wouldn't do it," Cuomo told CNN early in the day.
At a news conference later, Cuomo said Trump was "clearly spoiling for a fight on this issue" and that he did not want a partisan battle, but added, "We don't have a king in this country, we have a Constitution and we elect the president."
Social distancing restrictions imposed since last month by governors in 42 states have crippled the US economy, with businesses forced to close and millions of Americans thrown out of work, casting a shadow over Trump's re-election hopes.
US DEATH TOLL NEARS 26,000
The US death toll from COVID-19, the highly contagious respiratory illness caused by the virus, topped 25,700 on Tuesday, out of more than 600,000 known US infections, according to a running Reuters tally.
Despite tentative signs in recent days that the outbreak was starting to ebb, the number of US deaths counted on Tuesday rose to at least 2,104, the highest toll yet in a single 24-hour period, with a few states left to report their latest totals.
David Reich, president of New York's Mount Sinai Hospital, said even if hospital admissions there had leveled off, it still remains an extraordinary time of strain for staff and resources.
"The plateau is not a very comfortable place to live," Reich said in a telephone interview. "So I don't think people should be celebrating prematurely."
Offering an expansive assessment of the powers of the presidency, Trump on Monday asserted he has "total" authority to decide on reopening the economy even though he earlier had deferred to the governors in putting social-distancing orders in place.
Cuomo, a Democrat whose state has been the epicenter of the US outbreak, and governors of six other northeastern states have announced they will formulate a regional plan to gradually lift restrictions. On the Pacific Coast, the governors of California, Oregon and Washington state announced a similar regional approach.
Trump, whose attacks on Democrats appeal to his conservative political base, posted tweets attacking Cuomo individually and Democratic governors in general.
"Tell the Democrat Governors that 'Mutiny On The Bounty' was one of my all time favorite movies," the Trump wrote on Twitter on Tuesday, referring to a classic film about a rebellion against the commanding officer of a British naval vessel in the late 18th century.
"A good old fashioned mutiny every now and then is an exciting and invigorating thing to watch, especially when the mutineers need so much from the Captain. Too easy!" Trump wrote.
Trump rejected the idea that governors should determine when and how to reopen state economies, insisting "the president of the United States calls the shots."
But governors had their own plans. California Governor Gavin Newsom and Oregon Governor Kate Brown, both Democrats, on Tuesday offered frameworks for eventually restarting public life and business in their states.
Some Republicans, including the governors of Ohio, Maryland and New Hampshire, also said states have the right to decide when and how to reopen.