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 U.S. 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. 

Kremlin spokesman Dmitry Peskov, asked about the U.S. 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 U.S. policy," the foreign ministry said.

"Proposals on tough retaliatory actions, which appear to have been discussed in Washington are even more unacceptable."

U.S. President Donald Trump on Monday questioned Iran's claim that it had nothing to do with the attacks in Saudi Arabia.

"Remember when Iran shot down a drone, saying knowingly that it was in their 'airspace' when, in fact, it was nowhere close. They stuck strongly to that story knowing that it was a very big lie. Now they say that they had nothing to do with the attack on Saudi Arabia. We'll see?" the president wrote in a post.

Earlier the same day, Trump just tweeted his promise to supply oil to U.S. allies, adding that "we don't need Middle Eastern Oil & Gas, & in fact have very few tankers there, but will help our Allies!"

He warned on Sunday that his country was "locked and loaded" for a potential response to the attack on Saudi Arabia's oil facilities. 

Yemen's Iran-backed Houthi rebels on Monday threatened to carry out more strikes and urged foreigners to stay away.  

"We assure the Saudi regime that our long hand can reach any place we want at any time we choose," Houthi military spokesman Brigadier Yahya Saree said in a statement. 

Strikes on two Saudi facilities Saturday halted half the kingdom's production and sent shock waves through energy markets. 

The European Union (EU) stressed its call for "maximum restraint" following the attack the same day. 

EU spokeswoman Maja Kocijancic told journalists: "We see them (the attacks) as a real threat to regional security, and at a time that tensions in the region are running very high this attack undermines ongoing work at de-escalation and dialogue."

Also on Monday, the Iraqi government said it had been told by the U.S. side that Washington did not suspect an attack on Saudi Arabia had been launched from Iraqi territory. 

U.S. Secretary of State Mike Pompeo had told Iraq's Prime Minister Adel Abdul Mahdi by phone "the information they have confirms the Iraqi government's statement that its territory was not used to carry out this attack."

Iraq is one of the few countries friendly with both Iran and the United States. Iraq's Popular Mobilization Forces, an umbrella of mostly Shi'ite paramilitary groups backed by Iran, are influential in parliament and have allies in government.

In response to recent attacks on Saudi Arabian oil facilities, Foreign Ministry spokesperson Hua Chunying said on Monday that China opposes any action that may intensify events in the Middle East. 

"In the absence of firm conclusions, it is irresponsible to assume who should be responsible," said Hua.

She also called on related parties to avoid radical actions and jointly safeguard regional peace and stability.

(With input from agencies)