Brent futures gained $1.01, or 1.4 percent, to settle at $71.24 a barrel, while U.S. West Texas Intermediate crude gained 74 cents, or 1.2 percent, to $61.78.
The 1,200-kilometre pipeline carries crude from Saudi Arabia's main eastern oil fields to the Red Sea port city of Yanbu in the west.
Drone war has escalated over the past months between Saudi Arabia, which has been leading an Arab coalition since March 2015 to support the Yemeni exiled government, and the Iran-allied Houthi rebels who seized much of Yemen's north in late 2014.
Tuesday's attack also came amid unconfirmed reports that Houthi rebels were starting to unilaterally withdraw from the strategic Yemeni port of Hodeidah, a key condition of a December cease-fire that the United Nations and worldwide community see as a first step toward ending the war.
Al-Falih condemned the attacks as "an act of terrorism" that targeted global oil supplies and aimed to destabilize the worldwide energy supply.
"With rising tensions between Iran and the USA, and with significant naval build-up in the region, markets are sensitive to news and can be tipped by the smallest signs of a conflict", said Mihir Kapadia, chief executive of Sun Global Investments.
Iran recently threatened to resume higher enrichment in 60 days if no new nuclear deal is in place, beyond the 3.67% permitted by the current deal between Tehran and world powers.
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Mercredi également, se tiendra une réunion de ministres du numérique du G7, autour du secrétaire d'Etat au numérique Cédric O . Qwant, DailyMotion, la Fondation Wikimédia ont également adopté ce texte.
Sunni-ruled Saudi Arabia and Shi'ite majority Iran are regional rivals and oil from the kingdom was expected to compensate for the decline expected in Iranian exports.
Houthi spokesman Mohammed Abdel-Salam said Tuesday the strikes are a clear message to the Saudi Kingdom.
However, he added, Aramco had halted oil pumping in the pipeline while the damage was evaluated and the stations were repaired, according to Reuters. The official added that Saudi Aramco will assess the damage and fix the plants. Official numbers will be released by the U.S. Energy Information Administration later today.
This is not the first time the Houthis have used drones.
Asked at the White House about the incident, President Donald Trump responded: "It's going to be a bad problem for Iran if something happens".
Iran was a prime suspect in the sabotage on Sunday although Washington had no conclusive proof, a USA official familiar with American intelligence said on Monday.
Khamenei, Iran's supreme leader who has final say on all state matters, was quoted by state TV as telling senior officials that his country won't negotiate with the United States, calling such talks "poison".
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Amid rising fears of a conflict, here is what we know about Sunday's attacks off the Emirati coast. "They know that it is not to their benefit".
Washington's dispatch to the region of the USS Abraham Lincoln carrier group, an amphibious assault ship, a Patriot missile battery and B-52 bombers has sparked fears of possible military clashes.
Just days before the attack, the United States warned ships that "Iran or its proxies" could be targeting maritime traffic in the region.
However, the manager of one of the tankers that was hit said it suffered hole in its hull after an unknown object struck it off the U.A.E. coast. Images on Monday of the Norwegian-flagged Andrea Victory, which the company said was "not in any danger of sinking", showed damage similar to what the firm described.
The other two were crude oil tankers owned by the Saudi shipping firm Bahri.
A report out by the American Petroleum Institute on Tuesday showed that USA crude inventories increased by 8.6 million barrels last week, to 477.8 billion. The official was not authorized to discuss the investigation and thus spoke on condition of anonymity.
Iran's Foreign Minister Mohammed Javad Zarif said on Tuesday that he was anxious about "suspicious acts of sabotage now taking place in the region".
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The Gulf Cooperation Council condemned the tanker sabotage on Monday as a "serious escalation" that could "increase tensions and conflict in the region and jeopardize the interests of their peoples".