President Donald Trump has expressed hope coronavirus cases were "levelling off" in US hotspots, saying he saw "light at the end of the tunnel".
On Sunday, New York, the epicentre of the US outbreak, reported a drop in the number of new infections and deaths.
Mr Trump described the dip as a "good sign", but warned of more deaths as the pandemic neared its "peak" in the US.
"In the days ahead, America will endure the peak of this pandemic," Mr Trump said at his daily coronavirus briefing.
He said more medical personnel and supplies, including masks and ventilators, would be sent to the states that are most in need of assistance.
Deborah Birx, a member of the president's coronavirus task force, said the situation in Italy and Spain, where infections and deaths have fallen in recent days, was "giving us hope on what our future could be".
"We're hopeful over the next week that we'll see a stabilisation of cases in these metropolitan areas where the outbreak began several weeks ago," Dr Birx said at the same news conference.
Optimism from Dr Birx and Mr Trump contrasted with other leading US experts, including top advisor Dr Anthony Fauci, who earlier said the short-term outlook was "really bad".
The US surgeon general, meanwhile, warned that this will be "the hardest and the saddest week of most Americans' lives".
"This is going to be our Pearl Harbor moment, our 9/11 moment," Surgeon General Jerome Adams told Fox News on Sunday.
The US has reported 337,274 confirmed infections and 9,619 deaths from Covid-19, by far the highest tally in the world.
What's the latest in New York?
On Sunday, Governor Andrew Cuomo reported 594 new deaths giving an overall total of 4,159 deaths in New York, the state hit hardest by the coronavirus so far.
He said there were now 122,000 New York residents who had been infected. But he added that nearly 75% of patients who have required hospitalisation had now been discharged.
Patients requiring hospital are down for the first time in a week, and deaths are down from the previous day, he said.
There were 630 deaths reported in the previous 24 hours.
"The coronavirus is truly vicious and effective at what the virus does," he told reporters in Albany, the state capital.
"It's an effective killer."
It's too early to know if New York is currently experiencing its apex - the highest rate of infection that graphics behind Mr Cuomo referred to as "the Battle on the Mountain Top".
He also said it was too early to know if cases would drop off quickly after the apex, or if they would decline slowly - and at a rate that would still overwhelm hospitals.
"The statisticians will not give you a straight answer on anything," he said about the so-called "curve" - the chart that tracks the rate of infections.
"At first it was straight up and straight down, or a total 'V'. Or maybe its up with a plateau and we're somewhere on the plateau. They don't know."
In other developments around the world:
- UK Prime Minister Boris Johnson has been admitted to hospital, 10 days after he tested positive for coronavirus. He was expected to remain there overnight for what Downing Street described as "routine tests"
- The Queen has said the UK "will succeed" in its fight against the pandemic, in a rallying message to the nation
- In the UK's daily coronavirus briefing, Health Secretary Matt Hancock said he "cannot rule out further steps" being introduced in terms of social distancing - but that none are imminent
- Hours later, Scotland's chief medical officer, Dr Catherine Calderwood, resigned after it emerged she had visited her second home, despite the lockdown measures
- Italy reported that 525 people had died in the previous 24 hours - the lowest daily figure since 19 March
- Another 674 people died in Spain - the lowest daily death toll in over a week
- Millions of Indians have turned off their lights for a nationwide candle-lit vigil, heeding a call for unity as the country battles coronavirus
What is the situation around the US?
Infection rates and new deaths are growing in cities such as Washington DC, Detroit and New Orleans, even as around 90% of Americans are under some form of mandatory lockdown requiring them to stay home.
Governors of states continue to warn of a dire shortage of needed medical supplies, including ventilators and face masks.
New Jersey, a state that borders New York, reported more than 3,000 new infections on Sunday, bringing the state-wide total to 37,505. There have been 917 coronavirus-related deaths in New Jersey.
The southern state of Louisiana - one of the hardest hit in the US - reported a 20% increase on Sunday with 3,010 new cases. It also reported 477 deaths.
Michigan - with the third worst outbreak in the US - has suffered nearly 16,000 cases and 617 deaths, officials said on Sunday. Detroit continues to be the state's major hotspot with nearly 5,000 cases and 158 deaths.
Speaking to NBC News earlier on Sunday, Dr Anthony Fauci - the nation's chief immunologist - said it was too early to say the situation was "under control," as President Donald Trump has frequently claimed.
"That would be a false statement. We are struggling to get it under control and that's the issue that's at hand right now."
Surgeon General Adams said that California and Washington had seen their transmission rates slow due to mitigation efforts, but warned that everyone must follow the federal government's health guidance, including wearing a face mask in public.
"I want Americans to understand that, as hard as this week is going to be, there is a light at the end of the tunnel if everyone does their part for the next 30 days," he said.
What else did President Trump say?
President Trump devoted a large part of Sunday's news conference to discussing an anti-malaria drug being used to treat Covid-19 in the US.
The drug, hydroxychloroquine, had shown some "very strong, powerful signs" of its potential, Mr Trump said.
Most experts say hydroxychloroquine is an unproven, experimental treatment whose effectiveness in treating Covid-19 is not well understood.
Yet the US Food and Drug Administration (FDA) has approved the drug for "emergency use" in Covid-19 patients admitted to hospital.
Mr Trump said his administration had ordered 29 million doses of the drug, which were to be distributed across the US.
"If it does work, it would be a shame if we didn't do it early," Mr Trump said. "I'm not a doctor, but I have common sense."
Elsewhere in the US:
- Several governors say Mr Trump should issue a national 'stay-at-home' order, after nine mostly southern and Midwestern states have resisted enforcing a lockdown
- A tiger at the Bronx Zoo has tested positive for coronavirus and several other big cats are exhibiting symptoms. They are thought to have been infected by a zookeeper
- Mr Trump says he will defy the government's guidance to wear masks in public, after the Centers for Disease Control and Prevention announced the new mandate last week