New York (CNN) -- Sarah Shourd had been waiting for this meeting for 14 months, pleading for a private conversation with Iranian President Mahmoud Ahmadinejad while she was imprisoned in Tehran.

On Friday, she got it, meeting with the Iranian leader in New York where he was attending sessions at the United Nations.

"I would like to thank President Ahmadinejad for giving me and my mother, Nora, the opportunity to meet with him today," Shourd said in a statement issued by family spokeswoman Samantha Topping. "It was a very gracious gesture and a good meeting.

"While I was in prison, I pleaded for the chance to speak with President Ahmadinejad in order to clear up any misunderstanding that led to our detention."

The meeting came just hours after Shourd told CNN's "American Morning" that she hoped to meet with Ahmadinejad while he was in New York.

She said she wanted to make a personal appeal for the freedom of her fiance, Shane Bauer, and friend Josh Fattal, who remain jailed in Tehran's Evin Prison.

"I have no animosity towards him or the government," Shourd said. "I want it to be resolved. I want it to be finished."

No further details of the meeting were released.

Earlier Friday, Shourd recounted her experience while imprisoned in the Islamic republic.

Shourd told "American Morning" that she can still feel the hot tears rolling down her cheeks and the thud of a door slamming in her face as prison guards walked away from her cramped little cell.

And when she thinks about her freedom, it is always marred by the thought of Bauer and Fattal, still having to endure days without sunlight, being let out of their cell for only an hour a day to "exercise," or rather, walk side by side in what she described as the space of a towel.

She remembers how she begged to make a phone call, a request that was finally granted seven months into her captivity.

"By the time I got a phone call, I lost hope that it was going to happen," she told CNN.

Iran released Shourd on humanitarian grounds last week after Omani authorities posted her bail, set at $500,000. She returned home to the United States on Sunday with her mother by her side.

She spoke about the fateful events that landed her in one of the world's most notorious prisons.

She and Bauer were fascinated with the Middle East and wanted to immerse themselves in the region to learn more about it.

Shourd taught in Damascus, Syria, for a year but jumped at the opportunity to travel to Iraq's Kurdistan region in July 2009. Her eyes took in nothing but the drab hues of the Syrian desert. She wanted to feast on the greenery of Kurdistan, she said.

So the three Americans embarked on a hiking expedition. They were on a trail that ran behind a popular tourist site by a waterfall. She remembered families picnicking there.

The border was unmarked, Shourd said, and the three Americans did not realize they had strayed into Iran. Iranian authorities arrested them, accused them of spying and ordered them behind bars.

"Our story was completely unexpected and tragic," Shourd said. "We did nothing wrong. We meant no harm to the Iranian people. We would never risk our safety in that way and put our families through this."

She said the tension between the United States and Iran -- the two nations have no diplomatic ties -- heavily influenced the way things unfolded.

"I just think it's a huge misunderstanding -- more to do with the problems between the countries than us as individuals," Shourd said.

She wants Bauer and Fattal home for a host of reasons. At the top of that list is that she and Bauer have a wedding to plan.

She held up her right hand that bears an improvised enagagement ring that Bauer wove from thread. He proposed to her in prison.

She said Fattal stayed in the room he shared with Bauer so that Shourd and Bauer could spend time alone outside.

"I have something to tell you," Bauer told her.

"I hope it's not bad because I'm having a really bad day," she responded.

Instead, it turned out to be a beautiful moment for Shourd. Bauer told her that he asked her to marry him while they were imprisoned so that they could have something to sustain them through their days in Evin. It would keep alive their belief in the future.

It kept Shourd going then, and it keeps her going now, as she works to bring her fiance and friend home.

CNN's Mary Snow and Moni Basu contributed to this report.