Earlier on Tuesday, Ukraine slapped economic restrictions on Russia's largest internet group Yandex and other popular online firms, saying it wanted to guard against cyber threats, and the Kremlin threatened retaliation, as reported by Reuters.
"We have been witnessing Russia's response to the presidential decree that mentioned closing access to Russian social media. The website of the president is affected by an organized attack," the deputy head of the presidential administration, Dmytro Shymkiv, said in a statement.
"The situation is under control thanks to our IT-specialists and there is no threat to the work of the website," he said.
There was no immediate comment from the Kremlin.
The Ukrainian sanctions froze any assets held by the Russian businesses inside Ukraine and banned hosts there from linking to them, though the websites were all still accessible in Kyiv on Tuesday.
The ban was imposed partly to protect against companies "whose activities threaten the information and cyber security of Ukraine", the Kyiv government's Security and Defense Council said in a statement.
They added to a list of more than 400 Russian firms blacklisted by Kyiv since Moscow's annexation of Crimea in 2014 and the ensuing pro-Russian separatist uprising in eastern Ukraine.
Read alsoUkraine to block Russia propagandist media, social networks for three yearsMail.ru Group, which owns the Odnoklassniki social network and Vkontakte, Russia's version of Facebook, said that around 25 million Ukrainians could be affected by the "politically motivated" decision.
"We have never been involved in politics. We have not broken a single law of Ukraine," it said in a statement. It said the Ukrainian market contributed an "immaterial" amount of revenue and so Mail.ru would not revise its financial plans.
Yandex also said it did not expect the sanctions to have a material negative impact on its financial results. There was no immediate comment from other companies on the list.
Kremlin spokesman Dmitry Peskov told journalists that Moscow had not forgotten the principle of reciprocity when it came to such disputes, calling the move "short-sighted".
Many of the affected sites are hugely popular in Ukraine.
Vkontakte was the second-most visited website in Ukraine as of March, according to data cited by the Ukrainian Internet Association. Yandex, Odnoklassniki and Mail.ru were also in the top five most popular sites that month.
Read alsoInformational Policy Ministry brands banned Russian social networks "instruments of hybrid war"In comments to Russian newspaper Kommersant, Russian Foreign Ministry spokesman Maria Zakharova called the sanctions a "manifestation of politically motivated censorship".
Moscow has repeatedly denied accusations from Kyiv that it has been waging a "cyber war" against Ukraine. It also denies accusations that it is fueling the separatist conflict in eastern Ukraine by supporting rebels with troops and weapons.
Ukraine has also accused Russian computer hackers of targeting its power grid, financial system and other infrastructure with viruses.