Russia on Monday urged countries in the Middle East and outside the region not to draw "hasty conclusions" on who staged the attacks on Saudi oil facilities.
A senior US official said earlier that evidence from the attack, which hit the world's biggest oil-processing facility, indicated Iran was behind it, instead of the Yemeni Houthi group that had claimed responsibility.
US President Donald Trump said on Sunday the United States was "locked and loaded" for a potential response to the attack on Saudi Arabia's oil facilities.
Kremlin spokesman Dmitry Peskov, asked about the US statement, said: "We have a negative attitude towards rising tensions in the region and call for all countries in the region and outside of it to avoid any hasty steps or conclusions which may deepen destabilization."
In a separate statement on Monday, Russia's foreign ministry said it believed that the exchange of strikes on civilian targets was "a direct consequence of the ongoing sharp military and political crisis in Yemen".
"We believe it is counterproductive to use what happened to increase tensions around Iran in line with the well-known US policy," the foreign ministry said.
"Proposals on tough retaliatory actions, which appear to have been discussed in Washington are even more unacceptable."