MOSCOW (AP) — Russian authorities acknowledged Tuesday that a low number of coronavirus cases in the country could be a result of insufficient screening and warned that the nation must brace for the worst.

President Vladimir Putin donned a yellow protective suit to visit the top Moscow hospital treating coronavirus patients and conferred with officials on how to stem the outbreak. Hospital chief Denis Protsenko told Putin the country needs to "prepare for the Italian scenario.”

Russia has reported 495 cases and no deaths. Critics have argued for weeks that the numbers are too low for a country with a 2,600-mile border with China, blaming a low level of testing and a long tradition of hiding unpleasant truths.

At the same time the coronavirus was engulfing Europe, Putin ordered an April 22 plebiscite on constitutional amendments that could allow him to stay in power until 2036. But he also has said the vote could be postponed if the contagion spreads.

Some have accused the government of manipulating the statistics to downplay the coronavirus threat in order to prevent panic and ram the constitutional vote through at any cost.

“They themselves don't know how many actual cases they have, because testing is of such low quality” said Anastasia Vasilyeva, a doctor for Russian opposition figure Alexei Navalny and leader of the Alliance of Doctors union.

Vasilyeva and some others pointed at a 37% increase in pneumonia cases in Moscow in January as a sign that the figure could include some unreported coronavirus cases.

“We receive information from medical workers in the regions. ... Hospital beds are full with these, supposedly, pneumonia cases patients,” she said.

The authorities have denied tweaking or concealing coronavirus statistics and argued that the increase in pneumonia cases could have been explained by a more proactive screening for pneumonia this year.

Officials have ranted about "fake news" of covered-up deaths and said that those spreading them could face criminal charges. On Tuesday, Vasilyeva said the police were investigating her for claiming the government was manipulating statistics.

The government and some experts have credited the low number of cases on an early closure of the border with China and a ban on entry for Chinese citizens at the time the epidemic was at full swing in that country. Starting early this month, Russia also has requested all travelers from Italy, France and other countries worst affected by the virus to self-quarantine for two weeks after arrival.

And finally last week, the Russian government has denied entry to all foreigners except diplomats and members of official delegations.

The Kremlin had sought to project an upbeat view on the situation, insisting that all measures have been taken to prevent a bigger outbreak. But on Tuesday, Moscow Mayor Sergei Sobyanin, who leads a task force on dealing with the virus, warned that the situation could be worse than it seems.

“The number of tests has been quite low and a real picture is not known,” Sobyanin said during a meeting with Putin, adding that provincial governors must receive orders to move more quickly to ready hospital beds for the gravely ill.

For most people, the virus causes only mild or moderate symptoms, such as fever and cough. For some, especially older adults and people with existing health problems, it can cause more severe illness, including pneumonia. The vast majority of people recover.

Sobyanin ordered all Moscow residents over 65 to stay home starting Thursday, voicing hope that this measure, along with other moves by the city authorities, will help to “flatten the curve” and prevent the nation's health care system from being overwhelmed with patients.

“Otherwise, the system won't be able to cope,” he said.

Doctors warn that Russia should brace itself for a major outbreak. “We are looking at tens of thousands of infections down the line at the very best,” Pavel Brand, the director of Klinika Semeynaya, a chain of private medical clinics in Moscow, told The Associated Press.

The government said 163,000 coronavirus tests have been performed so far. Until recently, all tests in Russia were analyzed by just one lab in Novosibirsk and it took several days to get results.

Sobyanin reported to Putin that Moscow this week launched its own network of labs, and that the number of tests will reach 13,000 a day for the city.

Moscow, a city of more than 13 million, already has shut schools, canceled public events, banned gatherings of more than 50 people and encouraged companies to make arrangements for employers to work from home — moves that already have been taken in other regions across Russia.

The authorities in the capital also ordered the construction of a new hospital for coronavirus patients that is being built from scratch and should be ready in several weeks. In addition to three hospitals treating coronavirus patients in Moscow, several other clinics have been recently converted for the purpose.

Dr. Melita Vujnovic, the World Health Organization representative in Russia, praised the measures taken in the country as “very effective.”

“The WHO recommendations from the very beginning are do not wait until it gets you and start doing it," she told the AP. "And this has been the trick or the secret in Russia delaying of the epidemic. For the moment, I would say, that the capacity is sufficient to absorb the initial growth.”

Many have voiced concern, however, that Russia's teetering, underfunded health care system could be hard pressed to cope with a big coronavirus crisis.

Many medical facilities were shut down in recent years as part of massive cost-cutting reforms, and wards for treating infectious diseases were always first to go, said Victor Maleyev, epidemiologist with Russia's Central Institute of Epidemiology. “So now they have to find beds elsewhere,” he said.

Another big problem appears to be shortages of protective gear. Medical communities on social media are abuzz with reports of doctors and nurses not being given enough face masks, and Vasilyeva said her union receives a lot of complaints about that.

More than 100,000 people have signed an online petition launched last week, demanding more action from the government and saying there might be “thousands, or even tens of thousands of people” infected with the virus. Among other things, the petition demanded transparency in telling people about the scale of the outbreak and the speed at which it spreads. “The authorities cannot and should not have secrets from the people,” the petition said.

Daniel Kozin in Moscow contributed.