Sarah Shourd, 31, her boyfriend Shane Bauer, 27, and Josh Fattal, 27, were arrested in July along the Iran-Iraq border, and Iran has accused them of espionage.

Their families say the three were simply hiking in Iraq's largely peaceful mountainous northern Kurdish region and that if they crossed the border, it was accidental.

But their detention has become entangled in the political confrontation between the US and Iran.

Iranian leaders have repeatedly suggested a link between their jailing and that of a number of Iranians by the US.

Further increasing tensions, the US announced before the mothers' arrival in Tehran that it had support from other major powers for a new round of UN sanctions against Iran over its refusal to stop uranium enrichment in its nuclear programme.

Reunion

The mothers - Nora Shourd, Cindy Hickey and Laura Fattal – had hoped to at least make a face-to-face appeal for their children's release to Iranian leaders, including Mahmoud Ahmadinejad, the president, or Supreme Leader Ali Khamenei.

Shafii said the mothers "were willing to stay longer" to meet Iranian officials but "the conditions were not right".

Iran said it allowed the reunion as a humanitarian gesture [AFP]

Instead, they were given two opportunities to see their children in the high-rise Estaghlal hotel near Evin prison, where the Americans were being held.

On Friday, the three were brought to their mothers' private rooms for several hours. Afterwards, the mothers were driven to the airport and left on a flight to Dubai.

Their children were taken back to Evin, witnesses at the hotel said.

Iran 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 on Thursday.

In the first public look at the three Americans since their detention, there were hugs, kisses, tears and a lavish meal in the hotel restaurant.

The three detainees, who appeared healthy, last had direct contact with their families in a five-minute phone call in March.

Iran has hinted in the past that it wants to swap the three Americans for a number Iranians being held by the US - including several who have been convicted in the US over violations of American sanctions on Iran.

Also among them is a nuclear scientist, Shahram Amiri, who disappeared during a visit last year to Saudi Arabia, raising speculation he defected to the West.

US: No swap

On Thursday, PJ Crowley, a spokesman for the US state department, told reporters in Washington that the US was "not contemplating any kind of a prisoner swap" for the three Americans.

"But if Iran has questions about any of its citizens and whether we have any information as to their whereabouts, we would be more than happy to receive that diplomatic note and respond to it," he said.

The two Iranians who were released from custody in Iraq on Friday were identified as Ahmad Barazandeh and Ali Abdolmaleki, who had been held for seven and two years respectively, for entering Iraq without a passport, Iran's ambassador to Baghdad said, according to a report on Iranian state TV.