Russian authorities do not know the full extent of the coronavirus outbreak across the country and should step up measures to stem the pandemic, a top official said Tuesday.

Russia, which shares a with China and has a population of 144 million, has officially reported 495 cases of the coronavirus but no confirmed fatalities.

"The problem is that the volume of testing is very low and no one has a clear picture" of the situation in Russia and the world, Moscow Mayor Sergei Sobyanin told President Vladimir Putin during a meeting.

"The picture that is unfolding is serious," said Sobyanin, who heads an anti-coronavirus task force at Russia's State Council.

He said the number of people infected with the coronavirus was "significantly" higher than official figures.

Taking the day to discuss the epidemic, Putin later visited Moscow's new infectious diseases clinic, where he donned a hazmat suit and met head doctor Denis Protsenko.

He warned the president that Russia may be headed for the Italian scenario of a spike in heavy cases and fatalities, particularly in Moscow.

"It is important to prepare for the 'Italian' scenario. If there is a big spike, and Moscow is headed there, our hospital is ready to transform," he said.

If new cases "suddenly" flatline, doctors will be overjoyed, but "we must still prepare for the worst," he told Putin.

Putin said last week that the outbreak is under control in Russia.

The country has gradually tightened restrictions, halting cultural and sports events and closing schools and fitness clubs.

It has also closed borders to almost all non-citizens.

Sobyanin on Monday requested that older Muscovites stay at home and on Tuesday told Putin that other regions should follow suit.

However, unlike many countries in Asia and Europe, the has not ordered any confinement.

"Not all regions understand" the seriousness of the situation, Sobyanin said. "Regardless of whether they have or not they all should get ready."

He singled out the Far East's Primorsky Region, which shares a border with China, saying that if thousands of people travelled across the border recently then "it's a problem, a big problem".

Sobyanin added: "And sooner or later the problem will rear its head."