The three women - Nora Shourd, of Oakland, Calif.; Cindy Hickey, of Pine City, Minn.; and Laura Fattal, of suburban Philadelphia - returned to New York on Saturday afternoon aboard an Emirates flight from Dubai that landed John F. Kennedy International Airport.
Shourd thanked the Iranians for allowing the women to see the three. She said the women were disappointed they could not return with their children and that "the pain is almost more than we can bear."
Hickey said, "We will forever favor the precious moments we were able to spend with our children."
"Our greatest hope was to bring our children home with us where they belong," said Hickey. "We will hope and pray that the Iranian authorities will now find it in their hearts to resolve our children's case, and release them without delay."
The detained Americans are 31-year-old Sarah Shourd, her 27-year-old boyfriend, Shane Bauer; and their friend, 27-year-old Josh Fattal. They've been held in Iran since July after being arrested along the Iraqi border.
Iran accused them of espionage; their families say the three were hiking in Iraq's northern Kurdish region and that if they crossed the border, it was accidental.
The mothers returned to New York after a "very emotional goodbye" to their children, the brother of one captive told The Associated Press.
"They're managing to cope with an extremely difficult situation," said Alex Fattal, brother of Josh Fattal. "We're waiting to give them a hug here in New York and to hear more."
Alex Fattal said about a dozen family members around the country - in California, Florida, New York, Pennsylvania, Minnesota and Colorado - had a half-hour conference call with the mothers on Friday after they arrived in Dubai from Tehran.
The women told family members they had spent a total of about 10 hours with their children over two days in Iran but failed to secure their release, said Alex Fattal, who is on leave from a doctoral program in anthropology at Harvard University so he can help gain the Americans' release.
"They have mixed feelings," he said. Friday, the day they left Tehran, "was a tremendously emotional day for them and for us; it was very difficult for them to leave, an extremely difficult departure after a very emotional goodbye."
The mothers had hoped to at least make a face-to-face appeal for their children's release to Iranian leaders.
The Swiss ambassador in Iran told AP Television News there were no negotiations with Iranian officials to free their children. Washington and Tehran broke off diplomatic relations following the 1979 Islamic Revolution, and Switzerland handles U.S. interests in Iran.
"The point was that they should see their children. They have seen them quite a lot over the last two days," Ambassador Livia Leu Agosti said late Friday in an interview at the Tehran airport after the mothers left the country. "It was a visit to the children. That was the purpose."
Asked whether there were any positive signs from Iranian authorities, Agosti told APTN: "Well, they were very generous in the time that the allotted the mothers to be with their children. So it was a good gesture."
Iran announced Friday that two of its nationals held in Iraq by U.S. forces for years were freed, raising the possibility that a behind-the-scenes swap was in the offing or that their release was a gesture of goodwill in an attempt to free the Americans.
The Iranians' release "may have some diplomatic effect on this case," the Americans' lawyer, Masoud Shafii, told the AP.
The U.S. has said it is not offering a direct swap, and Iranian officials made no public connection between the freed Iranians and the Americans.
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Iran has said it allowed the mothers to visit the Americans as a humanitarian gesture, and state TV gave heavy coverage to the mother's first reunion with their children Thursday. They embraced, kissed and cried, then sat for a lavish meal in the hotel restaurant. It was the first public look at the three young Americans since their detention.
Josh Fattal told reporters, "We hope we're going home soon, maybe with our mothers."
But that didn't happen.
"Generally, we continue to hold out hope," Alex Fattal told the AP. "We know our loved ones are innocent, and we hope the Iranian authorities will recognize that."
The three appeared healthy in TV coverage, wearing jeans and polo-style shirts. Sarah Shourd wore a maroon head scarf. They described their routines behind bars and being allowed books, letters from home, the ability to exercise and the one hour each day they are all together.
They are all graduates of the University of California at Berkeley. The last direct contact with their families had been a five-minute phone call in March.