ANKARA/BAGHDAD (Reuters) - Sixteen Turkish workers abducted by militants in Iraq arrived back in Turkey to emotional scenes on Wednesday night after more than a month in captivity.

The men were snatched on Sept. 2 from a stadium they were building on the outskirts of Baghdad, apparently by an armed group that used a familiar Shi'ite Muslim slogan and threatened to attack Turkish interests in Iraq if its demands were not met.

They were released earlier on Wednesday, before being flown from Baghdad back to the Turkish capital, where they were greeted by Deputy Prime Minister Yalcin Akdogan and other senior officials.

The families of the hostages waved Turkish flags as the men, many in tears, disembarked from the plane.

"I've missed my dad," one young girl who gave her name as Ayse Malek said as she waited on the tarmac.

Speaking to reporters, the men said they had been released by their captors with no explanation outside Baghdad, and had then been collected by the Turkish ambassador to Iraq, Faruk Kaymakci.

"They treated us very well where they kept us, we didn't have any problems. We were released because of the government, we're very thankful," one of the workers, Coskun Yilmaz, said.

Their release had been promised in an online video on Tuesday, after the United Nations backed a deal to extricate Syrian villagers under siege from rebels supported by Turkey.

SOLDIER IN HANDS OF ISLAMIC STATE

Ambassador Kaymakci earlier in the day told Reuters that no terms of release had been discussed with the kidnappers.

In a series of tweets from New York where he is attending the United Nations General Assembly, Prime Minister Ahmet Davutoglu said he had spoken to some of the men by telephone since their release.

"Thankfully, they are in good health and are preparing to return (home) in the shortest possible time," Davutoglu stated.

Baghdad has struggled to rein in Shi'ite armed groups, seen as a critical deterrent against Islamic State militants who control large swathes of the north and west.

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The city has also seen a proliferation in recent years of well-armed criminal gangs carrying out contract killings, kidnappings and extortion.

This is not the first hostage crisis Turkey has suffered. Last year Islamic State took 46 Turkish nationals hostage in the Iraqi city Mosul, before releasing them unharmed after more than 100 days in captivity.

Earlier this month it was reported that a soldier who had gone missing close to Turkey's Syria border was in the hands of Islamic State.

The soldier's capture is potentially a major liability, coming as it does just months after Ankara finally stepped up its operations against the militants, opening its airbases to U.S.-led coalition warplanes.

(Reporting by Orhan Coskun and Yesim Dikmen in Ankara, Stephen Kalin in Baghdad and Humeyra Pamuk in Istanbul; Writing by Ayla Jean Yackley and Jonny Hogg; Editing by Ralph Boulton)