DOHA/BAGHDAD April 27 (Reuters) - Qatar has denied trying to pay ransom money this month to secure the release of 26 Qataris abducted in Iraq a year and a half ago by unidentified gunmen, in a complex saga that has highlighted the Gulf state's strained ties with Baghdad.

Iraqi Prime Minister Haider al-Abadi said on Tuesday authorities had seized suitcases containing hundreds of millions of dollars on a private Qatari jet that landed in Baghdad. He suggested the funds were part of a deal to free the hostages without Baghdad's approval.

The 26 Qataris, including members of the country's ruling royal family, were abducted during a hunting trip in southern Iraq in 2015. They were released last Friday. urn:newsml:reuters.com:*:nL8N1HT32B

Qatar's foreign minister, Sheikh Mohammed bin Abdulrahman al-Thani, told Doha-based Al Jazeera late on Wednesday that Baghdad had been consulted about the money he said was sent "to support the authorities in the release of Qatari abductees".

"Qatar has provided funds to Iraq in an official, clear and public manner," Sheikh Mohammed said. "Qatar did not deal with armed groups outside the authority of the (Iraqi) state."

It was the first official statement made by the normally secretive government in Doha since the release of the 26 men, who were abducted in Iraqi territory dominated by militias aligned with neighbouring Shi'ite power Iran. urn:newsml:reuters.com:*:nL8N1HT32B

Their release was a boost for tiny Qatar, which has used its influence to free Western hostages in Middle East war zones.

The deal followed complex negotiations between Qatar, Iran and the Lebanese Shi'ite group Hezbollah, and was linked to the evacuation of four besieged Syrian towns, according to a Qatari official. urn:newsml:reuters.com:*:nL8N1HT32B

Qatar and other Gulf states view Abadi's government as close to Iran, their main regional rival, while Baghdad accuses Doha of funding Islamist militants in the Syrian and Iraqi conflicts. Qatar, which is also part of the U.S.-led coalition fighting Islamic State, denies supporting militant groups.

Abadi angrily criticised Qatar's decision to send money.

"Sending the cash in this way is wrong ... legally wrong. What would happen if hundreds of millions of dollars went to the armed groups Is this acceptable" he said at a news briefing.

No one has claimed responsibility for the abduction of the 26 Qataris, seized near a Saudi border area dominated by Shi'ite militias who have accused Doha of meddling in Iraq's affairs.

Qatar had urged Iraq to take the lead in freeing the hostages, who had been granted permits by Baghdad to hunt in the area. Iraq's interior ministry said the hunters had failed to heed government instructions to stay within secured areas.

Hunters from rich Gulf states travel to Iraq's desert in the winter months to buy falcons and hunt the rare houbara bustard, a bird whose meat is highly prized.

(Reporting by Tom Finn in DOHA and Ahmed Rasheed in BAGHDAD; Editing by Gareth Jones) ((Tom.Finn@thomsonreuters.com))