Speaking at a press conference this afternoon in New York City, Shourd appeared with her mother, Nora Shourd, and with the mothers of Shane Bauer and Josh Fattal, who remain jailed in Evin Prison in Tehran.
The three young people were picked up along the Iran-Iraq border last year and were accused of spying.
Shourd said that she, her fiancé Bauer and friend Fattal never spied or committed any crime, and called their arrest "a huge misunderstanding."
"This is not the time to celebrate," Shourd, 32, said in prepared remarks. "The only thing that enabled me to cross the gulf from prison to freedom alone was the knowledge that Shane and Josh wanted with all their hearts for my suffering to end."
Shourd thanked Iranians and Ahmadinejad in a carefully scripted return that spoke to the continuing delicacy of her situation. Iran has issued espionage-related indictments against her, Bauer and Fattal; the indictments could bring trials for the two men and proceedings in absentia for Shourd.
But she stressed their innocence in a case that has added to the roster of tensions between the U.S. and Iran.
Meanwhile, Iranian President Mahmoud Ahmadinejad arrived in New York to attend the U.N. General Assembly. He later met with U.N. Secretary-General Ban Ki-moon to discuss developments in Iraq, Afghanistan and the Middle East as well as efforts to resolve the dispute over Iran's nuclear program, the U.N. spokesperson's office said.
He called Shourd's release "a huge humanitarian gesture" in an interview on "This Week with Christiane Amanpour." He called on the U.S. to release eight Iranians being detained after arrests he said were illegal.
The three Americans were detained in July 2009 after Iranian officials said they intentionally crossed the country's border from Iraq. Echoing accounts their families have given in their absence, Shourd said Sunday that the three had been hiking in a popular tourist area - near a waterfall in Iraq's Kurdistan region - and had no idea the border was nearby.
"If we were indeed near the Iraq-Iran border, that border was entirely unmarked and indistinguishable," she said.
"Shane and Josh do not deserve to be in prison one day longer than I was," she 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 arrest and prolonged detention."
Shourd's mother has said she had health problems including a breast lump and precancerous cervical cells. Shourd said Sunday that doctors in Oman, where she went immediately after her release, had determined she was physically well.
Officials in Oman - an ally of both Iran and the United States - mediated a $500,000 bail for Shourd that satisfied Iranian authorities and apparently did not violate U.S. economic sanctions against Iran. The source of the bail payment has not been disclosed.
Shourd and Bauer had been living together in Damascus, Syria, where Bauer was working as a freelance journalist and Shourd as an English teacher. Fattal, an environmental activist and a fellow graduate of the University of California at Berkeley, came to visit them last July, and the three went hiking.
"My hope is that by learning who we are and how we came to be in this diverse and fascinating region of the world directly from my lips, it will help clear up any doubts and end Shane and Josh's detention," Shourd said.
She added that she hoped their experience would provide "an opportunity for Americans and Iranians to realize that an improved relationship would be in the best interest of all people."
Sarah's mother, Nora Shourd, also spoke: "Yesterday was my birthday, and I have received the greatest gift of all. But Cindy and Laura are still waiting for their gifts. And this is why I applaud the humanity that set Sarah free, and I cry 'Encore, encore.' It's time for Shane and Josh to come home, too. And we will not stop until they are home and we will redouble our efforts to get them out."
Ahmadinejad gave no specifics in his interview with Amanpour about whether Bauer and Fattal might also be released, saying "the cases have to be examined."
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