Britain's own prime minister, Boris Johnson, was hospitalized, 10 days after testing positive for COVID-19 in what his office described as a "precautionary step."
Amid the dire news, there were also glimmers of hope some hard-hit areas - the number of people dying appeared to be slowing in New York City, Spain and Italy. The news was cautiously welcomed by leaders, who also noted that any gains could easily be reversed if people did not continue to adhere to strict lockdowns.
The U.S. is still awaiting the peak, and Surgeon General Jerome Adams offered a stark warning about the expected wave of virus deaths.
"This is going to be our Pearl Harbor moment, our 9/11 moment,'' he told "Fox News Sunday."
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In a rare televised address to her country, meanwhile, Queen Elizabeth II also appealed to Britons to rise the occasion, while acknowledging enormous disruptions, grief and financial difficulties.
"I hope in the years to come, everyone will be able to take pride in how they responded to this challenge," she said. "And those who come after us will say that the Britons of this generation were as strong as any."
In New York City, the U.S. epicenter of the pandemic, daily deaths dropped slightly, along with intensive care admissions and the number of patients who needed breathing tubes inserted, but New York state Gov. Andrew Cuomo warned that it was "too early to tell" the significance of those numbers.
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Italy and Spain also got some encouraging news. Italy registered its lowest day-to-day increase in deaths in more than two weeks - 525, said Angelo Borrelli, the head of the national Civil Protection agency. The pace of infection also seemed to be slowing.
Even so, Borrelli warned, "This good news shouldn't make us drop our guard."
Confirmed infections fell in Spain, too, and new deaths declined for the third straight day, dropping to 674 - the first time daily deaths have fallen below 800 in the past week.
"We are starting to see the light at the end of the tunnel," Spanish Prime Minister Pedro Sánchez said.
The outlook, however, remained bleak in Britain, which reported more than 600 deaths Sunday, surpassing Italy's increase. Italy still has by far the world's highest coronavirus death toll - almost 16,000.
Johnson, meanwhile, has been hospitalized, though his office said it was not an emergency and that the 55-year-old Conservative will undergo tests.
There are concerns that Johnson's government did not take the virus seriously enough at first and that spring weather will tempt Britons and others to break social distancing rules.
Health Secretary Matt Hancock said the U.K. might even ban outdoor exercise if people still ''flout the rules.''
"The vast majority of people are following the public health advice, which is absolutely critical, and staying at home," Hancock told Sky TV. "But there are a small minority of people who are still not doing that - it's quite unbelievable, frankly, to see that."
As the numbers of infections rose, the deputy head of Britain's National Health Service Providers said the agency needed to focus on quickly increasing ventilator capacity and getting more protective equipment for health care workers.
"I think that we are just a week away from the surge of this,'' Saffron Cordery told Sky TV.
Italians have not been immune to lure of the good weather either. Top Italian officials took to national television after photos were published showing huge crowds out shopping in Naples, Rome, Genoa and even the hard-hit Veneto city of Padua.
Health Minister Roberto Speranza told RAI state television that all the sacrifices Italians have made since the nationwide lockdown began on March 10 risked being reversed.
Restrictions on movement vary from country to country. In Germany and Britain, residents can get out to exercise and walk their dogs, as well as go to the supermarket, the post office and do other essential tasks. Yet in Serbia and South Africa, dog walking is not allowed.
In France, heat-seeking drones have been whizzing over Fontainebleau forest to identify rule-breakers after the former royal estate in the Paris suburbs was closed to the public.
In Sweden, authorities have advised the public to practice social distancing, but schools, bars and restaurants are still open.
At the Vatican, Pope Francis celebrated Mass and blessed palms for Palm Sunday in a near-empty St. Peter's Basilica. Usually tens of thousands of faithful would have crowded the square outside.
In New Orleans, Rev. Emmanuel Mulenga blessed palm fronds and put them on a table near the back of his Saint Augustine Catholic Church - so people could get them while also observing social distancing.
Worldwide, more than 1.2 million people have been confirmed infected and nearly 70,000 have died, according to Johns Hopkins University. The true numbers are certainly much higher, due to limited testing, different ways nations count the dead and deliberate under-reporting by some governments.
The vast majority of infected people recover from the virus, which is spread by microscopic droplets from coughs or sneezes. For most people, the virus causes mild to moderate symptoms such as fever and cough. But for some, especially older adults and the infirm, it can cause pneumonia and lead to death. The World Health Organization says 95% of the known coronavirus deaths in Europe have been in people over 60.
The rapid spread of the virus in the United States has prompted a chaotic scramble for medical equipment and protective gear.
An Associated Press review of federal purchasing contracts showed that federal agencies largely waited until mid-March - more than two months after the first warnings of a potential pandemic - to begin placing bulk orders of N95 respirator masks, mechanical ventilators and other equipment needed by front-line health care workers.
By that time, hospitals in several states were treating thousands of infected patients without adequate equipment and pleading for shipments from the national stockpile. Now that stockpile is nearly drained just as the numbers of patients requiring critical care is surging.
Rebekah Gee, who heads the Louisiana State University's health care services division, warned that the private and public sector have been competing with each other, leading to price increases.
Gee, who once ran the state's Department of Health, said one of her colleagues went on eBay to buy gowns, while equipment her department ordered from China got stalled for weeks in Hong Kong.
"Our whole country is at war with this virus," she said. "This needs a coordinated approach, and right now that's not happening."
Louisiana and the New Orleans area have been hard hit by the virus, and Gov. John Bel Edwards has repeatedly warned of looming shortages for ventilators and intensive care unit beds.
Dr. Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, said Sunday that he hoped the pace of new infections would plateau soon, but that the virus is unlikely to be completely eradicated this year.
Speaking on CBS's "Face the Nation," Fauci said the prospect of a resurgence is why the U.S. is working so hard to develop a vaccine and conducting clinical trials on treatments.
This is the first known outbreak of the virus, and scientists are still learning about it. In what is believed to be the first known infection in an animal in the U.S., officials said Sunday that a tiger at the Bronx Zoo had tested positive for the virus.
ABC Owned Television stations contributed to this report.