By Rania El Gamal

DUBAI (Reuters) - Saudi Arabia said on Thursday it was suspending oil shipments through the Red Sea's Bab al-Mandeb strait, one of the world's most important tanker routes, after Yemen's Iran-aligned Houthis attacked two ships in the waterway.

Brent futures rose 19 cents to $74.12 a barrel by 1305 GMT, extending their rally into a third day but slipping from a 10-day high in earlier trading. [O/R]

Saudi Arabia and arch-foe Iran have been locked in a three-year proxy war in Yemen, which lies on one side of the Bab al-Mandeb strait at the southern mouth of the sea, one of the most important trade routes for oil tankers heading from the Middle East to Europe.

The Houthis, who have previously threatened to block the strait, said on Thursday that they had the naval capability to hit Saudi ports and other Red Sea targets. Iran has threatened to block another strategic shipping route, the Strait of Hormuz.

Saudi Energy Minister Khalid al-Falih said the Houthis attacked two Saudi oil tankers in the Red Sea on Wednesday, one of which sustained minimal damage.

"Saudi Arabia is temporarily halting all oil shipments through Bab al-Mandeb strait immediately until the situation becomes clearer and the maritime transit through Bab al-Mandeb is safe," he said.

It was not clear if a Saudi-led military coalition would take additional security measures or impose further restrictions on imports to Yemen, which is struggling with the world's most urgent humanitarian crisis.

A senior oil source said Saudi Arabia had already beefed up oil security and that all crude vessels in the area are accompanied by security ships.

Saudi crude exports through Bab al-Mandeb are estimated at around 500,000-700,000 barrels per day (bpd), according to analysts and Reuters data. Most Gulf oil exports that transit the Suez Canal and SUMED Pipeline pass through the strait.

(For a graphic on 'Saudi Arabia issues temporary halt on shipments of its crude through Red Sea strait' click https://reut.rs/2LF3NCD)

Story continues

The chairman of the Kuwait Oil Tanker Company said the country was considering whether to follow suit.

The commander of Iran's Revolutionary Guards Quds force, Qassem Soleimani, criticised the U.S. role in the Red Sea.

"The Red Sea, which was secure, is no longer secure with the American presence ... (U.S. President Donald) Trump should know that we are nation of martyrdom and that we await him," Soleimani was quoted as saying on Thursday.

Industry and shipping sources said the suspension was unlikely to impact Saudi crude supplies to Asia, but could add shipping costs to Saudi vessels heading to Europe and the United States due to a longer transit.

Traders said the suspension order was only for Saudi-owned vessels, so state-owned Saudi Aramco could still charter foreign ships to move its crude.

Saudi Arabia also has a pipeline route to the city of Yanbu on the Red Sea keeping Europe and North America well supplied -- the 5-million-bpd Petroline.

The world's largest oil exporter has kept its crude shipments flowing during previous regional conflicts, including the 1980-1988 Iran-Iraq war when the two sides sought to disrupt each other's oil exports in what was known as the Tanker War.

The OPEC heavyweight, a key U.S. ally, has led a pact among oil producers to boost output to cool the market after Trump imposed sanctions on Iran and criticised OPEC for high prices.

Saudi state media reported shortly after Falih's announcement that the kingdom's Crown Prince Mohammed bin Salman chaired a meeting of the Political and Security Affairs Council but did not mention what topics were discussed.

Saudi Arabia leads a coalition of Sunni Muslim Arab states which intervened in Yemen's war in 2015 to restore the internationally recognized government in exile and thwart what Riyadh sees as Tehran's expansionist ambitions in the region.

HODEIDAH IS KEY

Saudi Arabia and the United Arab Emirates backed Trump's decision to quit a nuclear deal with Iran. They accuse Iran of supplying the Houthis with weapons including missiles, which the group and Tehran deny.

The latest attack on Saudi oil tankers could strengthen the Arab states' position ahead of possible U.N.-sponsored peace talks between Yemen's warring parties, which aim to avoid an all-out assault on the country's main port city of Hodeidah.

The Western-backed military alliance launched an offensive on June 12 to wrest Hodeidah from the Houthis in a bid to cut off the primary supply line of the movement, which holds the most populated areas of Yemen including the capital Sanaa.

But the alliance did not make major gains and on July 1 it halted operations to give the United Nations a chance to resolve the situation in Hodeidah and the wider conflict which has killed more than 10,000 people.

"The only way forward is to get Hodeidah. What we are planning to do is give diplomacy every possible chance to secure that," Anwar Gargash, the UAE's minister of state for foreign affairs, said in London.

The United Nations fears that cutting off Hodeidah may trigger a famine in Yemen, where around 8.4 million people are believed to be on the verge of starvation.

The United Nations says the Houthis have offered to hand over management of the port to the world body, but the Saudi-led coalition says that the Houthis must quit the western coast.

One of the coalition's main justifications for intervening in Yemen was to protect shipping routes such as the Red Sea. It has said it foiled previous attacks there in April and May.

The Bab al-Mandeb strait is only 18 miles (29 km) wide, making hundreds of ships potentially an easy target. The U.S. Energy Information Administration said an estimated 4.8 million bpd of crude oil and products flowed through it in 2016.

(Additional reporting by William James, Aziz El Yaakoubi, Hesham Hajali, Florence Tan and Jonathan Saul; Writing by Ghaida Ghantous; Editing by Sonya Hepinstall and Giles Elgood)