The official further noted that despite the incident, the production and export of Saudi oil would continue "without interruption".
The pumping stations reportedly targeted lie west of the capital Riyadh, at Dawadmi and Afeef.
On Tuesday morning, the Houthi group announced the implementation of a major military operation "using drones" against Saudi targets.
On Tuesday, Saudi energy minister Khalid Al Falih said two pumping stations and a pipeline linking the oil-rich eastern province with the industrial city of Yanbu had come under attack by drones carrying explosives.More news: Prince Harry reveals how Meghan Markle is coping as a new mum
The minister said these attacks prove again that it's important for the Saudi government to face terrorist entities, including the Houthi militias in Yemen that are backed by Iran.
In the face of growing global concern, US Secretary of State Mike Pompeo scrapped a planned visit to Moscow and headed to Brussels instead for talks Monday with European officials, as Britain warned of the danger of conflict erupting "by accident" in the Gulf.
A picture taken on May 13, 2019 off the coast of the Gulf emirate of Fujairah shows Norwegian oil tanker Andrea Victory, one of the four tankers damaged in alleged "sabotage attacks" in the Gulf the previous day. "It's not in [Iran's] interest, it's not in our interest, it's not in Saudi Arabia's interest to have a conflict".
Heshmatollah Falahat Pisheh, the head of Iran's National Security Foreign Policy Committee, said in an interview with Iranian state media Monday that "Iran and the United States can manage the crisis by themselves".
Riyadh said its two tankers suffered "significant damage" but there was no oil spill.
The U.S. has sent forces, including an aircraft carrier and B-52 bombers, to the Middle East in a move that officials said was to counter "clear indications" of threats from Iran to American forces in the region.More news: Meghan celebrates first Mother's Day with Archie on United States date
"If they do anything, it would be a very bad mistake", Trump warned at the White House.
The exact details of the attack remain unclear, but investigators believe that Iranian agents or one of Tehran's regional proxies used explosives to blow large holes in the ships.
USA officials have so far given no details on exactly what happened to the ships and have no proof of who was responsible.
It is not known whether the two incidents are linked.
Washington suspects Iran but Tehran has denied any involvement. "Absolutely. But we have not planned for that", Trump said.
His comments resonate with those of the head of the Revolutionary Guard's air force Amir Ali Hajizadeh who called the move a "serious threat" and said that if the U.S. chose to make a move, Iran would be forced to retaliate.More news: Pregnant woman shot, killed by Texas officer during struggle over Taser
The damage occurred off the UAE port of Fujairah, which is the UAE's only terminal located on the Arabian Sea coast, bypassing the Strait of Hormuz, a global shipping route through which most Gulf oil exports pass. Iran has repeatedly threatened to close the strait if it is involved in a military confrontation with the US.
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