Sarah Shourd spent more than 13 months in captivity. Before leaving Oman, she expressed appreciation and hope to the nation that helped broker her release.
"I will always associate your country with the first breath of my freedom," she said.
Shourd arrived in Oman Tuesday. The Arab nation, an ally of both the U.S. and Iran, mediated the $500,000 bail that was part of Shourd's release. It may have saved her life. Her mother says Shourd has a lump on her breast and pre-cancerous cervical cells.
"Please, please extend your prayers to my fiancé, Shane, and good friend Josh," said Shourd.
She leaves behind the men she was arrested with last year, her fiancé, Shane Bauer and their friend Josh Fattal. All three were accused of spying in July 2009 after Iran claimed they crossed the border, reports CBS News correspondent Michelle Miller.
"These two men have been held without cause," said Secretary of State Hillary Clinton. She says she's continuing diplomatic negotiations for their freedom through third parties.
"It would be a very significant humanitarian gesture for the Iranians to release them," said Clinton.
On Iranian television, President Mahmoud Ahmadinejad called on America to offer the olive branch. He wants the release of 11 Iranians he claims are being held captive by the U.S.
Shourd made no mention of her year-long ordeal inside Tehran's notorious Evin prison. She chose instead to talk about the future.
"It would be a pleasure to return to Oman. It would be my deepest hope that I would be able to show Shane and Josh the grand mosque soon, one of the most peaceful and powerful places I've seen."
Shourd will have a news conference in New York Sunday. Supporters say it was timed to coincide with the Iranian president's arrival in the U.S. He's set to attend the U.N. general assembly.
More on the Imprisoned American Hikers:
Oman: No Plans to Free 2 Americans Still in Iran
Freed U.S. Hiker Sarah Shourd Lays Low in Oman
Freed U.S. Hiker Reunited With Mother
Sarah Shourd Freed, Arrives in Oman
Mothers of Hikers Still in Prison: It's Our Turn
Katie Couric Interviews Josh Fattal's Brother
Mothers of Imprisoned Hikers Speak Out