Family spokeswoman Samantha Topping confirmed the meeting with Ahmadinejad, who was in New York to attend the United Nations General Assembly. Topping declined to say what was discussed.
"I'm just going to keep pushing every minute for their release on humanitarian grounds," Shourd told ABC News outside a hotel after she and her mother, Nora Shourd, met with the president.
Shourd, 32, called the encounter "a very gracious gesture and a good meeting," and said Ahmadinejad seemed friendly and that it was "a very human encounter, very personal."
Iranian U.N. Counselor Mohammad Reza Bak Sahraei confirmed with CBS News foreign analyst Pam Falk that Shourd and her mother met with Ahmadinejad saying, "It was a good meeting, it was brief, and she thanked the president for her release."
Shourd came to New York to advocate for the release of her fiance, Shane Bauer, and their friend Josh Fattal, who remain imprisoned in Tehran after 14 months.
Shourd told The Associated Press on Thursday of the monotony, cramped quarters and fears for her future during her 410 days in an Iranian prison, mostly in solitary confinement.
In one of her first interviews since her Sept. 14 release from Tehran's notorious Evin Prison, she said that she chooses to savor the few moments of joy she found in her imprisonment.
One of her happiest days, she said, was the celebration of her 32nd birthday last month. Somehow the men, who remain in Tehran's notorious Evin Prison, had persuaded a guard into bringing her the cake and even found a way to give her a whiff of liberty.
They talked her through a whole imaginary day that they called a "freedom walk" from waking up and having pancakes, to going to a lake, then walking to her mother's apartment. When they came to the part of their story where the apartment door opened, Bauer and Fattal spun Shourd around.
"They had brought all the pictures we had of our family and put them on these boxes, so everyone was there, and it was a surprise party. It was beautiful," she said, her voice catching. "I cried."
But most days in prison were far more monotonous or terrifying.
She recalled how the three made a vow while blindfolded in a prison van shortly after their capture: If they were separated, they would go on hunger strike until they were reunited.
Shourd starved herself for four days, lying alone in her cell and growing weaker. In prison, she kept reviewing her last day of freedom. What could they have done differently? What if, when they asked a tea vendor near a waterfall for advice on a hiking path, they had gone another way?
On the fourth day, the hikers were reunited for five minutes. Shourd began eating again, but their captivity was just beginning.
Alone in her cell, Shourd began going over multiplication tables in her head. It was the only way she could keep out thoughts of her mother. Of whether she knew where her daughter was. Of how worried she must be. Of whether they would see each other again.
If she thought of her mother, she began to fall apart, Shourd recalled.
"I just had to be sure that I was strong when I went into the interrogation room because I wanted to make sure that I didn't, that they didn't manipulate me into saying anything that I didn't want to say," she said.
She wondered whether she'd be hurt. If suddenly the door might open and she'd be dragged away.
Instead, a few times a day, a female guard would come bearing layers of extra clothing and a blindfold, so when Shourd arrived at the interrogation room she couldn't see the faces of her questioners.
She was amazed at their "good cop, bad cop" approach, just like on TV shows back in the U.S.
They had her write down what felt like every detail of her life, from her childhood in Los Angeles to her time living with Bauer in Syria, where she taught English and Bauer, a native of Onamia, Minn., was a freelance journalist. Fattal, who grew up in Pennsylvania, had come to the Middle East to visit them.
Over two months, she wrote hundreds of pages, she said. When she would finish writing an answer to a question, an interrogator would tell her "this is not good enough" and tear up her words. She would write again, and again hear the pages tear.
"I would just write it the same every time," she said.
They questioned her about her e-mails and about her Skype contacts, looking for any indication she had intended to come to Iran.
Shourd says she'd been missing the green mountains of the U.S. after a year in Syria. She and Bauer had heard from friends that the lush lands of northern Iraq had been largely untouched by the war, so they and Fattal traveled to Ahmed Awa waterfall, where they found hundreds of Kurdish families eating at restaurants and camping.
The first indication they were near the Iran border was three hours into their hike when they met Iranian officials on a trail leading from the waterfall. By then, it was too late.
Shourd tried to resist her imprisonment at first. She constantly yelled, cried or begged her captors for a phone call. She was confined to her 10-foot-by-5-foot cell. At night, the bit of sunlight from the window would dim, but the lights stayed on.
Eventually, the interrogations ended. The two men were moved into a cell together. The three Americans were allowed to see each other, at first for 30 minutes each day, then for an hour, then for two.
The trio had local TV, including 15 minutes of English-language news every day. They received a bundle of letters from their parents and siblings about once a month. And they had books in English. Shourd read the Quran, using her basic Arabic to communicate haltingly with some Farsi-speaking guards about religion.
Shourd would spend all day saving up details to tell the other two. At first, the three went over what they called "reruns" reviewing every memory of their lives in tremendous detail. When those ran out, they started to dream of the future and what they would do on the outside.
Some plans were bigger than others.
On one evening, Bauer asked Fattal to stay in their cell during their allotted time outdoors, so that the couple could have a moment alone.
The two sat on a rough wool mat, cockroaches skittering around them and dust filling the air. They held hands, and Bauer asked her to marry him. He made them engagement rings from two thin pieces of string.
"It's not what every person thinks of as romantic, but it was romantic for me," Shourd said.
And now, she is back on the outside, appearing on "The Oprah Winfrey Show," preparing for a tour of TV studios, a bit of string tied around her finger.
She feels some guilt, she said, but she pushes that aside. She learned in prison how to ignore negative emotions.
She thinks of the men, of the strong, supportive faces they put on when they learned only she would leave. She still doesn't know who paid her $500,000 bail, though she said an Omani official told her of an Iranian citizen who attempted to mortgage his home to pay it.
Ahmadinejad had told the AP that he hoped Bauer and Fattal would be able to provide evidence that "they had no ill intention in crossing the border" so that they can be released.
Iran has issued espionage-related indictments against the three of them, which could bring trials for the two men and proceedings in absentia for Shourd, although she says she hasn't ruled out returning to face trial.
She wants the world to see Bauer and Fattal, who are passing long days in a cramped space not much larger than a towel.
Shourd said they exercised to stay sane. There were days she would force herself to run or do jumping jacks despite the tears streaming down her face.
The men got even more inventive. They would lift their beds. They would stockpile water bottles, fill them with water, pile them into bags and lift them. They were intent on staying strong.
Part of her wishes she were still with them. Out here she can't protect them. She doesn't know that the books are still available or whether the guards are still being kind.
"The only thing that gives my freedom meaning is that I have this work to do, because honestly if I felt like there was nothing to do out here, if I wasn't needed in so many ways, I would have rather stayed with them," she said.
But out here, she can be their voice. She can do her best to make sure the world doesn't forget. She will be tireless, she said.
And until they're at her side, "my life will not resume."
Earlier Friday, Ahamedinejad maintained that Iran would consider ending uranium enrichment, the most crucial part of its controversial nuclear activities, if world powers send Tehran nuclear fuel for a medical research reactor.
Addressing a packed press conference in a New York hotel, Ahmadinejad also said Iran was prepared to set a date for resumption of talks with six world powers to discuss Tehran's nuclear program, saying October would be the likely time for the two sides to meet.
in which he claimed most people in the world believe the United States was behind the Sept. 11, 2001 terror attacks and again challenged the United Nations to set up a commission to probe the attacks.
"I did not pass judgment, but don't you feel that the time has come to have a fact finding committee?" Ahmadinejad asked.