British Prime Minister Boris Johnson was in intensive care Tuesday with the coronavirus, while Japan's leader declared a monthlong state of emergency for Tokyo and six other regions to keep the virus from ravaging the world's oldest population.

The 55-year-old Johnson, the world's first head of government known to have fallen ill with the virus, was in stable condition and conscious at a London hospital, where he was receiving oxygen but was not on a ventilator, said his spokesman James Slack. Foreign Secretary Dominic Raab was designated to run the country in the meantime.

"We're desperately hoping that Boris can make the speediest possible recovery," said Cabinet minister Michael Gove, who is among scores of British officials in self-isolation. Johnson's pregnant fiancee is recovering from coronavirus symptoms.

Japan's prime minister made the emergency declaration after a spike in infections in Tokyo, but it was a stay-at-home request — not an order — and violators will not be penalized. Despite having relatively few infections and deaths, Japan is a worrying target for a virus that has been killing the elderly at much higher rates than other age groups.

Deaths in the U.S. reached about 11,000, with around 370,000 confirmed infections.

In New York and in some European hot spots, authorities were hoping that plateaus in deaths and new hospitalizations meant that the outbreak was turning a corner.

In Spain, one of the hardest-hit countries, new deaths Tuesday rose to 743 and infections climbed by 5,400 after five days of declines, but the increases were believed to reflect a weekend backlog. Authorities said slowing the contagion will be a long process and were confident in the downward trend.

Italy's commissioner for fighting the COVID-19 virus appealed to Italians ahead of Easter weekend not to lower their guard and to abide by a lockdown now in its fifth week.

Citing data that shows that pressure on Italian intensive care wards is easing, Domenico Arcuri said that ''the cruel reality is stronger that algorithms.''

''Don't ever forget even for an instant that this invisible, strong and unknown virus has taken 16,523 lives through yesterday,'' Arucuri said, reciting the figure repeatedly. ''I beg you, in the next hours and days, do not cancel this number from your memory.''

New coronavirus cases were also slowing in France and Portugal. To keep up social distancing, Paris banned daytime jogging just as warm spring weather settled in.

U.S. Surgeon General Jerome Adams said that if Americans continue to practice social distancing for the rest of April, "we will be able to get back to some sense of normalcy."

"I want the American people to know there is a light at the end of this tunnel, and we feel confident that if we keep doing the right thing for the rest of this month, that we can start to slowly reopen in some places," he said on ABC's "Good Morning America."

One lockdown exception in the U.S. was Wisconsin, which asked hundreds of thousands of voters to ignore a stay-at-home order to participate in its presidential primary Tuesday.

In New York, Gov. Andrew Cuomo announced the first, faint signs that the outbreak there  may be nearing its peak. But h e cautioned against relaxing social distancing restrictions and warned that the health care system is still under extreme pressure.

"This is a hospital system where we have our foot to the floor and the engine is at red line and you can't go any faster," Cuomo said.

The state has averaged just under 600 deaths daily for the past four days, a horrific toll that was still seen as a positive sign because it was relatively steady. Cuomo also said the number of new people entering hospitals has dropped, as has the number of critically ill patients needing ventilators.

The U.S. government's top infectious-disease expert, Dr. Anthony Fauci, was cautiously optimistic, saying that in New York, "what we have been doing has been working."

Stocks climbed in early trading on Wall Street on Tuesday as markets around the world piled on even more big gains following their huge rally a day earlier. The S&P 500 index rose 3% in the first few minutes of trading and added on to Monday's 7% surge, following encouraging signs that the coronavirus pandemic may be close to leveling off in some of the hardest-hit areas of the world.

China, the first country to go into lockdown and among the strictest, reported no new deaths over the past 24 hours for the first time since it began publishing statistics on the virus that emerged in December in the city of Wuhan. Many experts, however, have been skeptical of China's virus figures. The final travel restrictions in  Wuhan are being lifted Wednesday.

Worldwide, more than 1.3 million people have been confirmed infected and over 75,000 have died, according to Johns Hopkins University. The true numbers are almost certainly much higher, because of limited testing, different rules for counting the dead and deliberate underreporting by some governments.

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. Close to 300,000 people have recovered worldwide.

One of the main models on the outbreak, from the University of Washington, is now projecting about 82,000 U.S. deaths through early August, or 12% fewer than previously forecast, with the highest number of daily deaths occurring on April 16.