Two of 18 Turkish workers kidnapped by gunmen in Baghdad this month have been freed in the southern province of Basra, Turkish and Iraqi officials said on Wednesday.

The men were among 18 employees of major Turkish construction firm Nurol Insaat kidnapped on September 2 in the Sadr City area of north Baghdad, where they were working on a football stadium project.

The kidnapping was claimed by an unknown militant group that presented itself as Shiite, and top cleric Grand Ayatollah Ali al-Sistani has demanded that they be released.

The Turkish ambassador to Iraq, Faruk Kaymakci, said that two workers had been released and were found near a Turkish company's premises in Basra.

"They are in good health," he told AFP. "They said the other 16 were also in good health as of yesterday (Tuesday)."

The Basra police issued a statement saying that the two men were found late on Tuesday, while the Turkish foreign ministry spokesman also confirmed their release.

"Two of our 18 fellow citizen abducted in Baghdad have been released. The two released workers are Necdet Yilmaz and Ercan Ozpilavci," spokesman Tanju Bilgic told the Dogan news agency.

The militant group that claimed the kidnappings, which identified itself as Furaq al-Mawt, or "Death Squads," issued a list of demands it said Ankara must fulfil for them to be freed.

The group said Turkey must order rebel forces to stop besieging four Shiite villages in northern Syria, stop militants from travelling from Turkey to Iraq, and cut the flow of "stolen oil from Kurdistan through Turkish territory."

- Demands to Erdogan -

Iraq's autonomous Kurdish region is independently exporting oil via Turkey in a move the federal government considers illegal -- a point of contention between Baghdad and Ankara.

"If (President Recep Tayyip) Erdogan and his party do not respond, we will crush Turkish interests and their agents in Iraq by the most violent means," the group said in the video.

Sistani, the top Shiite cleric in Iraq, who is revered by millions, said the kidnapped Turks must be freed.

"We demand the release of the kidnapped men and the end of such practices, which harm the image of Islam" in general and Shiites in particular, Sistani's office said in a statement.

Dozens of Turks have been kidnapped but later released in Iraq in the past 18 months by the Islamic State (IS) jihadist group, which overran large parts of the country last year.

But Sadr City, where the 18 Turks were kidnapped, is a stronghold of Shiite paramilitary forces opposed to the jihadists.

A soldier was killed last week when security forces clashed with the Shiite Ketaeb Hezbollah militia while searching for a person allegedly involved in the kidnappings.

The security command responsible for the capital said there had been intelligence that "one of the members of the gang that carried out the kidnapping" was on Baghdad's Palestine Street.

It did not identify the gunmen, but Al-Etejah television, which is affiliated with Ketaeb Hezbollah, said one of the group's facilities had been attacked by the Baghdad Operations Command on that street.

Baghdad turned to mostly Shiite volunteer forces for support as IS advanced towards the capital in June 2014. Those groups have played a key role in halting and then reversing the jihadists' gains.

In doing so, the government empowered Shiite militias, some with chequered human rights records, and spurred the creation of new ones, allowing them to act with near-impunity despite the fact they officially fall under government command.