"Such incidents can undermine the foundations of the world economy. That's why it's hardly possible to accept baseless accusations in this situation," said Kremlin spokesman Dmitri Peskov.
"We always urge a sober appraisal of the situation and to wait for more or less convincing evidence to appear," Peskov said on Russian television, extracts of which were published by the RIA Novosti news agency.
A Japanese and a Norwegian oil tanker were targeted in attacks on Thursday in the Gulf of Oman.
No one has claimed responsibility for the attacks.
The official Iranian news agency IRNA said the attacks took place within 30 nautical miles of Iran's coastline.
Iran rejected US accusations it was to blame, with Foreign Minister Mohammad Javad Zarif tweeting that the US had "immediately jumped to make allegations against Iran without a shred of factual or circumstantial evidence".
Saudi Arabia, Iran's arch-rival in the region and the world's top oil exporter, joined Washington in accusing Tehran of the attacks, with Saudi Crown Prince Mohammed bin Salman saying he "won't hesitate" to tackle any threats to the kingdom.
For his part the speaker of the Iranian parliament, Ali Larijani, hinted Sunday that Washington could be behind the "suspicious" tanker attacks in order to pile pressure on Tehran, IRNA reported.
Moscow "severely" condemned the attacks, he said, warning against drawing "hasty conclusions".