An official Omani news agency report said Oman's minister for foreign affairs, Oman's US ambassador, and the US ambassador to Oman attended the meeting but gave no further information about the discussions.
Speaking to reporters earlier, a US official said Clinton was expected to thank Qaboos for helping to arrange for Iran's release last month of US hikers Josh Fattal and Shane Bauer, who had been held in Iran after being arrested near the Iraq-Iran border in 2009, the official said.
The pair had been arrested along with fellow US hiker Sarah Shourd, who left Iran in September last year after being granted bail on humanitarian and medical grounds. As with her two jailed friends, Shourd's bail had also been set at $500,000 and was paid through Oman, a US Gulf ally that maintains friendly relations with Iran, their lawyer said.
The State Department official, who spoke to reporters on the flight to Muscat, said Clinton was also expected to follow up on talks she had with Qaboos here in January about social and economic reforms as well as development and education.
Omanis voted on Saturday to elect their purely consultative Majlis Al-Shura council, which Sultan Qaboos has pledged to vest with new authorities in response to unprecedented social unrest.
The official said Clinton also planned to sound out the sultan on the bloody violence in fellow Arab countries Syria and Yemen where authoritarian rulers have used deadly force against pro-democracy movements. Yemen neighbors Oman.
He said Clinton also wanted to share with him US concerns about Iran's behaviour, particularly an alleged Iranian plot -- unveiled by US officials last week -- to murder the Saudi ambassador in Washington. "We would expect that the 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," the US official told reporters.
Clinton arrived in Oman after paying brief visits to Malta as well as Libya, where she sought to promote the democratic transition pledged by the opposition who overthrew Moamer Kadhafi in August.