Russia and President Vladimir Putin are facing a "very problematic" situation as the coronavirus outbreak accelerates in the country, the Kremlin's spokesman told CNBC on Tuesday.

"It's a huge challenge and a huge danger for every nation in the world. It's not only about Putin or about Russia, every country is facing this challenge and it's quite unprecedented, we have never faced it before," Kremlin spokesman Dmitry Peskov said.

He noted that it was the first major international pandemic situation that anyone — including Putin — had faced.

"For him it's a challenge because we know that besides the danger for human life and health, this pandemic crisis will open the gates for a huge economic crisis in the world and this will be another challenge," Peskov added.

The coronavirus spread from China to Europe early this year but appears to have taken longer to take hold in Russia. Putin addressed the nation on March 25, telling them that the country could neither "insulate itself" from the threat of the coronavirus nor stop it from "spilling over" into the country from its neighbors.

He also canceled a referendum on constitutional changes that could allow him to serve additional terms in office, and declared a "nonworking week," which has since been extended to the end of April, to try to delay the spread of the virus. The Russian capital Moscow and major city St. Petersburg went into lockdown, as did other parts of the country.

But the number of confirmed cases of the virus is accelerating rapidly in Russia. On Sunday, the country of around 146 million people saw its largest daily rise in new confirmed cases — 6,060. Then on Monday, it reported 4,268 cases, prompting hopes of a slowdown, before the figures surged again Tuesday, with a rise of 5,642 cases, according to data from Russia's crisis response center.

Russia confirmed 5,236 new cases on Wednesday, bringing the country's official tally to 57,999. Nonetheless, the official death toll remains strikingly low — 513 people.

Peskov said the situation "is really extremely serious, it's very challenging, it's very problematic, it causes trouble to peoples all over the world, including Russia's."

He added that it was important to maintain unity within the international community, and a determination to overcome the crisis, noting that "this is the only way."

Some analysts have told CNBC that Russia was slow to respond to the crisis and that it's uncertain how its health-care system, which one expert described as "ailing," will manage. But Putin's spokesman defended Russia's approach, saying it had already started to check hospital capacity and equipment after the outbreak in China at the beginning of the year.

"Now ... the daily rise in figures is quite significant unfortunately, but it's not a rise that would jeopardize the health-care system," Peskov insisted, adding that Russia believes it will see a peak in infections in coming months and is looking for the number of new infections to level off in mid-May.

"Then we'll be expecting a gradual decline in figures," he added.