(CNN) -- Sarah Shourd, the American hiker released from an Iranian prison, told reporters Sunday that doctors in Oman have assured her that she is "physically well."
Reading from a prepared statement, Shourd expressed thanks to Iranian government and religious leaders, including Ayatollah Ali Khamenei and President Mahmoud Ahmadinejad, for her release after 410 days.
"It is my deepest hope that the world will not let this humanitarian gesture ... go unrecognized," she said. "I believe this decision is a step in the right direction for all of us."
However, she and the mothers of the other two detained Americans, Shane Bauer and Josh Fattal, called for their release. The two men remain in Tehran's Evin Prison.
Accompanied by her mother, Nora Shourd, Sarah Shourd arrived in the United States early Sunday on at Washington Dulles International Airport on a flight from Dubai. She had been expected to arrive in New York, but Samantha Topping, a spokeswoman for the hikers' families, said flights to New York were booked with travelers attending the United Nations General Assembly.
The two women drove with Fattal's brother, Alex, from Washington to New York to hold Sunday's news conference, appearing with Cindy Hickey, mother of Bauer, and Fattal's mother, Laura Fattal.
Shourd initially was taken to Oman after leaving Iran.
The three Americans were arrested in 2009 after they allegedly strayed across an unmarked border into Iran while hiking in Iraq's Kurdistan region.
"Shane and Josh don't deserve to be in prison one day longer than I do," Shourd said. "We committed no crime, and we are not spies. We in no way intended any harm to the Iranian government or its people and believe a huge misunderstanding led to our detention and prolonged imprisonment."
She said the three were unaware of the border while hiking, and if they did cross it, it was unmarked and indistinguishable.
"I never in my worst nightmare imagined I would be a prisoner," Shourd said. "I never saw it coming. And I never imagined my family would have to suffer like this."
She said boarding the plane in Tehran was one of the most memorable moments of her life, but her disappointment at being unable to share it with Bauer, her fiance, and Fattal was "crushing."
"I stand before you today only one-third free," she said. "That was the last thing that Josh said to me, before I walked through the prison doors. Josh and Shane felt one-third free at that moment, and so did I." She said the only thing that allowed her to cross "the gulf" into freedom was that "Shane and Josh wanted with all their hearts for my suffering to end. They showed nothing but joy at my release and that, more than anything, is testament to the selflessness and beauty of their spirits."
"I walked out of prison with my spirit bruised but unbroken," she said, "and I am more determined than ever that Shane and Josh, God willing ... will walk out the same way."
"I'm filled with joy and relief that my daughter is home, but my heart is still heavy with sadness that Shane and Josh are still in prison," Nora Shourd told reporters. She said Saturday was her birthday and she's received "the greatest gift of all," but noted Hickey and Laura Fattal are still awaiting their gifts.
Shourd said she does not blame the Iranian people for her detention, saying she found them to be a "diverse and generous people ... Like all of us, they love their families and they want to live in peace."
She said at the time of their arrest, she and Bauer were living in Damascus, Syria, where he was working as a journalist and she was teaching English to Iraqi and Palestinian refugees, as well as Syrian nationals. Fattah, an environmental teacher, had arrived in Damascus as their guest, she said. The three were drawn together by their humanitarian work in different areas, Shourd said.
Shourd said she wants to clear up the misunderstanding that led to the hikers' imprisonment, and believes "that now is the time to make the world a little safer for everyone through peace and dialogue."
She appealed to supporters to stand behind her "so that we can make this final push" for Bauer and Fattal's freedom together, and asked governments and others to help with the process of cooperation and bridge building. "Please help us create an atmosphere of good will," she said.
Shourd took no questions after reading her statement, answering, "No, thank you," to a reporter's shouted question -- whether she has a message for Bauer.
Shourd had a pre-existing gynecological problem, and her family said she also had a lump in her breast, her attorney Masoud Shafii said earlier.
Ahmadinejad, who this week described the release of Shourd as a humanitarian gesture, told Iranian state TV IRINN on Friday that Tehran has "no expectation" following her release. But he said in an interview broadcast Sunday that the United States should now release eight Iranians being held in America.
Ahmadinejad told the ABC program "This Week" that his ability to free Bauer and Fattal was limited, and that they will have to face Iranian justice for illegally entering his country.
"I will make a recommendation ... but at the end of the day, they violated the law," Ahmadinejad said in translated remarks.
On the same program, Secretary of State Hillary Clinton expressed relief for Shourd's release and called for Iran to also release Bauer and Fattal.
Asked about Ahmadinejad's statements, Laura Fattal said that while she and Hickey are anxious for the return of their children, they will not get involved in politics. "We are mothers, not politicians," she said. She said she was encouraged by Shourd's release.
"It is a mixed blessing," she said. "I'm very happy for her, but I want Josh home and I want Shane home."
Hickey told reporters they have requested a meeting with the Iranian president and "we're hopeful that we get one."
"We're going to be full steam ahead," she said. "We're going to continue this process until they're home."
CNN's Susan Candiotti contributed to this report.