WASHINGTON (REUTERS) - Three US citizens who were kidnapped in Baghdad last month have been released with the help of the Iraqi government, the State Department said on Tuesday.

Unknown gunmen seized the trio from a private apartment in the capital's southeasterly Dora district in mid-January and were thought to be held by an Iranian-backed Shi'ite militia, though Iraqi Prime Minister Haider al-Abadi later dismissed the likelihood of Iranian involvement.

"We sincerely appreciate the assistance provided by the government of Iraq, and its whole-of-government effort to bring about the safe release of these individuals," State Department spokesman Mark Toner said in a statement.

US Defence Department spokesman Peter Cook said the Americans were contractors for the State Department and said the Pentagon was not involved in the Americans' recovery.

An official in the Iraqi interior minister's office said the Americans had been released in an area near Yousifiya, south of Baghdad.

"Intelligence forces received them and will hand them over to the American authorities (in Baghdad)", he told Reuters earlier on Tuesday.

The Defence Department is providing the Americans with transportation out of the region, and they are set to leave Iraq on Tuesday, Cook said.

The Iraqi government has struggled to rein in the Shi'ite militias, many of which fought the US military following the 2003 invasion and have previously been accused of killing and abducting American nationals.

Some analysts believe the kidnappings were meant to embarrass and weaken Abadi, who is trying to balance Iraq's relations with rival powers Iran and the United States.

The names of two of the men are Wael al-Mahdawy and Amro Mohammed, according to a source familiar with the matter.

The third man's name has not been made available.