Kaspersky estimated that there had been more than 2,000 attacks, linked to a version of malware called Petya — 60 percent of them in Ukraine and 30 percent in Russia, including the country’s largest oil company.

But Kremlin spokesman Dmitry Peskov said “no serious problems” had occurred as a result of the cyberattacks. Speaking on a conference call Wednesday, Peskov also said he had no accurate information on the origin of the attacks.

But the damage was worst in Ukraine, and some Ukranian officials had initially expressed suspicions that the attacks originated in Russia. The hacks targeted government ministries, banks, utilities and other important infrastructure and companies nationwide, demanding ransoms from government employees in the cryptocurrency bitcoin.