Pompeo and bin Salman "agreed that this was an unacceptable and unprecedented attack that not only threatened Saudi Arabian national security, but... the world's energy supply in general", Efe news quoted State Department spokesperson Morgan Ortagus as saying in a statement on Wednesday.
They also agreed on "the need for the international community to come together to counter the continued threat of the Iranian regime and agreed that the Iranian regime must be held accountable for its continued aggressive, reckless, and threatening behaviour", the statement said.
The attacks on September 14 was carried out by 10 unmanned aircraft. It hit the Hijra Khurais - one of Saudi Arabia's largest oil fields, producing about 1.5 million barrels a day - and Abqaiq, the world's biggest crude stabilization facility, which processes seven million barrels of Saudi oil a day, or about 8 per cent of the world's total output.
Although the Yemeni Houthi rebels have claimed responsibility for the attack, Pompeo hortly after the attacks had denied it, saying: "There is no evidence the attacks came from Yemen", while blaming Iran instead.
Tehran has denied responsibility.
Parallel to Pompeo's visit, Middle East Strategic Alliance (MESA) partners Bahrain, Jordan, Kuwait, Oman, Qatar, Saudi Arabia, the United Arab Emirates and the US held meetings on Tuesday and Wednesday in Washington.
In a joint statement, MESA partners reported that during the meetings they addressed the attack against Saudi refineries "sought to disrupt oil markets and regional stability".
"The attack underscores the continuing importance of cooperation between the MESA partners to strengthen regional security, peace, and stability, promote and expand economic opportunities, and strengthen and secure critical energy sectors," they added.
( With inputs from IANS )