On a day trip scheduled after Iran shot down a US drone, Pompeo flew into the Red Sea city of Jeddah and met with King Salman at his palace.
Russian President Vladimir Putin will visit Saudi Arabia, a traditional US ally in the Middle East, in October this year, Saudi Energy Minister Khalid al-Falih said on Monday.
Their Highnesses the Supreme Council Members and Rulers of the Emirates sent separately cables of condolences to the Custodian of the Two Holy Mosques, King Salman Bin Abdulaziz of Saudi Arabia,
Two-hundred survivors and relatives from the Christchurch mosque shootings are traveling to the hajj pilgrimage in Saudi Arabia this week as guests of King Salman.
The 130-year-old pilgrim was invited by the Custodian of the Two Holy Mosques King Salman Bin Abdulaziz Al Saud to perform Hajj this year as part of the King Salman's Hajj and Umrah Guests Programme.
Secretary of State Mike Pompeo and other US officials were headed to Saudi Arabia
The meeting in Riyadh, where Esper arrived late on Monday after an unannounced visit to Afghanistan, also took in defence issues and the current situation in the region.
Russian President meetse Saudi King and Crown Prince as he seeks to cement Moscow's political and energy ties across the Mideast.
Khan on Sunday held talks with Iran's President Hassan Rouhani and supreme leader Ayatollah Ali Khamenei in Tehran, where he stressed the importance of avoiding such a conflict.