A key Gulf ally, Oman helped secure since September 2010 the release of three US hikers jailed in Iran, two of them last month, earning gratitude from the United States.
Now Washington is hoping to tap into Oman's influence with the Islamic republic of Iran and share US concerns about Iran's behaviour, particularly an alleged Iranian plot to murder the Saudi ambassador to Washington.
"We would expect that Omanis would use their relationship with Iran, as they have in the past, to help the Iranians understand the implications of what they're doing," a US State Department official said.
He told reporters on the flight to Muscat that Clinton would also discuss with Sultan Qaboos the brutal violence in Syria and Yemen, where authoritarian regimes are using deadly force against pro-democracy protesters.
She also formally thanked the ruler of the sultanate for helping secure the release last month of US hikers Josh Fattal and Shane Bauer, who were jailed in Iran after being arrested near the Iraq border.
Oman helped secure the release of all three US hikers, and paid their bail according to their Iranian lawyer.
President Barack Obama had earlier on Friday thanked Oman's Sultan Qaboos for his role in pushing Iran to free the US hikers.
Clinton arrived in Oman after paying brief visits to Malta as well as Libya.
She left the sultanate later in the evening on Wednesday and was seen off by Yousef bin Alawi bin Abdullah, Minister Responsible for Foreign Affairs, Sayyid Mohammed bin Salim al Said, Head of the Protocols Department at the Foreign Ministry, Hunaina bint Sultan al Mughairiyah, Sultanate's ambassador to the USA and Richard J Schmierer, USA ambassador to the Sultanate.