* Norwegian ship ablaze at sea, second tanker also abandoned
* Trump brief on attacks, Russia calls for caution
* Iran calls incidents "suspicious", urges dialogue
* Attacks occur during Japanese prime minister's Iran trip (Adds Pompeo due to speak at 1815 GMT)
By Lisa Barrington and Rania El Gamal
DUBAI, June 13 (Reuters) - Two oil tankers were attacked on Thursday and left adrift in the Gulf of Oman, driving up oil prices and stoking fears of a new confrontation between Iran and the United States.
The White House said President Donald Trump had been briefed and that the U.S. government would continue to assess the situation. Washington accused Tehran of being behind a similar attack on May 12 on four tankers in the same area, a vital shipping route through which much of the world's oil passes.
Tensions between Iran and the United States, along with its allies including Saudi Arabia, have risen since Washington pulled out of a deal last year between Iran and global powers that aimed to curb Tehran's nuclear ambitions.
Iran has repeatedly warned it would block the Strait of Hormuz, near where the attacks happened, if it cannot sell its oil due to U.S. sanctions.
No one has claimed Thursday's attacks and no one has specifically blamed them on any party.
U.S. Secretary of State Mike Pompeo is due to deliver remarks to the media at 1815 GMT, the State Department said without elaborating.
Iranian Foreign Minister Mohammad Javad Zarif described the incidents as "suspicious" on Twitter and called for regional dialogue. Tehran has denied responsibility for the May 12 attacks.
The Saudi-led military coalition, which is battling the Iran-aligned Houthis in Yemen, described Thursday's events as a "major escalation".
Russia, one of Iran's main allies, was quick to urge caution, saying no one should rush to conclusions about the incident or use it to put pressure on Tehran.
U.N. Secretary-General Antonio Guterres told a meeting of the U.N. Security Council on cooperation between the United Nations and the League of Arab States: "Facts must be established and responsibilities clarified."
He warned that the world cannot afford "a major confrontation in the Gulf region".
Council diplomats said the United States told them it planned to raise the issue of "safety and freedom of navigation" in the Gulf during a closed-door meeting of the Security Council later on Thursday.
"It's unacceptable for any party to attack commercial shipping and today's attacks on ships in the Gulf of Oman raise very serious concerns," acting U.S. Ambassador to the U.N. Jonathan Cohen told the U.N. meeting.
Crude prices climbed as much as 4% after the attacks near the entrance to the Strait of Hormuz, a crucial shipping artery for Saudi Arabia, the world's biggest oil exporter, and other Gulf energy producers.
"We need to remember that some 30% of the world's (seaborne) crude oil passes through the straits. If the waters are becoming unsafe, the supply to the entire Western world could be at risk," said Paolo d’Amico, chairman of INTERTANKO tanker association.
The crew of the Norwegian-owned Front Altair abandoned ship in waters between Gulf Arab states and Iran after a blast that a source said might have been from a magnetic mine. The ship was ablaze, sending a huge plume of smoke into the air.
The crew were picked up by a passing ship and handed to an Iranian rescue boat.
The second ship, a Japanese-owned tanker, was hit by a suspected torpedo, the firm that chartered the ship said. Its crew were also picked up safely. However, a person with knowledge of the matter said the attacks did not use torpedoes.
The Bahrain-based U.S. Navy Fifth Fleet said it had assisted the two tankers after receiving distress calls.
Iran has not openly acted on its threat to close the Strait of Hormuz even though U.S. sanctions have seen its oil exports drop from 2.5 million barrels per day in April last year to around 400,000 bpd in May.
Both sides have said they want to avoid war.
Bob McNally, president of the U.S. consultancy Rapidan Energy Group, said "we see this as Iran trying to get negotiating leverage it doesn’t have", and described the attacks as "upping the ante but not going all in".
"I don’t think it tips us over into direct military confrontation. It is still deniable and denied. This is still going to be like the attack last month – everyone is denying it. It’s a blunt message."
Japanese Prime Minister Shinzo Abe was visiting Tehran when Thursday's attacks occurred, carrying a message for Iran from Trump, who has demanded that the Islamic Republic curb its military programmes and its influence in the Middle East.
Abe, whose country was a big importer of Iranian oil until Washington ratcheted up sanctions, urged all sides not to let tensions in the area escalate.
Iran said it would not respond to Trump's overture, the substance of which was not made public.
Britain said it was "deeply concerned" about the attacks. Germany, which like Britain remains a signatory to the nuclear pact with Iran, said the "situation is dangerous" and all sides needed to avoid an escalation.
The Arab League said some parties were "trying to instigate fires in the region", without naming a particular party.
Oman and the United Arab Emirates, which have coastlines on the Gulf of Oman, did not immediately issue any public comment.
Saudi Arabia and the UAE, both majority Sunni Muslim nations that have a long-running rivalry with predominantly Shi'ite Iran, have previously said attacks on oil assets in the Gulf pose a risk to global oil supplies and regional security.
Bernhard Schulte Shipmanagement said the Japanese tanker Kokuka Courageous was damaged in a "suspected attack" that breached the hull above the water line while transporting methanol from Saudi Arabia to Singapore.
Japan's Kokuka Sangyo, owner of the Kokuka Courageous, said the ship was hit twice over a three-hour period.
A shipping broker said the vessel might have been struck by a magnetic mine. "Kokuka Courageous is adrift without any crew on board," the source said.
The crew of about 21 or 22 people was picked up by the Coastal Ace vessel, Denis Bross of Acta Marine in the Netherlands told Reuters. He said they were handed to a U.S. Navy vessel.
Taiwan's state oil refiner CPC said the Front Altair, owned by Norway's Frontline, was "suspected of being hit by a torpedo" around 0400 GMT carrying a Taiwan-bound cargo of 75,000 tonnes of petrochemical feedstock naphtha, which Refinitiv Eikon data showed had been picked up from Ruwais in the UAE.
Frontline said its vessel was on fire but afloat, denying a report by the Iranian news agency IRNA that the vessel had sunk.
Front Altair's 23-member crew abandoned ship after the blast and were picked up by the nearby Hyundai Dubai vessel. The crew was then passed to an Iranian rescue boat, Hyundai Merchant Marine said in a statement.
Iran's IRNA reported that Iranian search and rescue teams picked up 44 sailors from the two damaged tankers and took them to the Iranian port of Jask. The numbers in the Iranian media report could not be independently confirmed.
Iran’s state television showed what it said was a video of rescued crew members in Jask, showing them sitting on sofa, chatting and watching TV. There was one woman among them.
Thursday's attacks came a day after Yemen's Iran-aligned Houthis fired a missile on an airport in Saudi Arabia, injuring 26 people. The Houthis also claimed an armed drone strike last month on Saudi oil pumping stations.
Reporting by Koustav Samanta and Jessica Jaganathan in Singapore, Liang-Sa Loh and Yimou Lee in Taipei, Terje Solsvik in Oslo, Ghaida Ghantous in Dubai, Marwa Rashad in Riyadh, Michelle Nichols at the United Nations, Jessica Resnick Ault in New York; Hyunjoo Jin in Seoul and Jonathan Saul and Bozorgmehr Sharafedin in London; Writing by Edmund Blair and Alison Williams; Editing by Jon Boyle and Nick Tattersall