Mr Mabhouh was electrocuted and then strangled, reports said
Irish officials have met with Israel's ambassador to discuss the use of fake Irish passports by the alleged killers of a Hamas commander in Dubai.
Dubai police believe 11 "agents with European passports" killed Palestinian militant Mahmoud al-Mabhouh in January.
During Thursday's meeting, the Israeli authorities were requested to provide whatever information and assistance they could about the passports.
The ambassador said he had no information on the matter.
However, he said he would relay the messages he had received to his authorities.
Earlier the Irish government said the Irish passports had genuine numbers.
The Department of Foreign Affairs said the numbers on the passports corresponded to those on three real Irish passports.
However, the people identified in the passports recorded in Dubai were not those in the genuine passports.
Previously the department said the passport numbers were counterfeits, as they had the wrong number of digits and had no letters. It said it had since been given "additional material relating to the passport numbers".
Ireland's foreign minister, Micheal Martin said he was still trying to determine whether the three passports had been lost or stolen recently.
Two of the Irish people whose passport numbers were copied have been contacted and were due to travel this weekend.
Mr Martin said Interpol are on red alert and the two unsuspecting Irish citizens would likely have been arrested as they attempted to fly.
Speaking ahead of the meeting with the ambassador, Dr Zion Evrony, Mr Martin said: "We are putting fairly direct questions and seeking the assistance and clarifications.
"It's not for me to make declarations when there are inquiries under way, but certainly we want to get answers as quickly as we can."
He added: "It is an extremely serious incident and event and puts the security of Irish citizens at risk, there is no question of that."
After the murder of the Hamas man, police in Dubai issued arrest warrants for the 11 suspects.
The city's police chief said six of the suspects had British passports, three were Irish, one French and one German.
The three Irish suspects were identified as Gail Folliard, Evan Dennings and Kevin Daveron.
Officials in Dubai said the team appeared to be a professional hit-squad, most likely sponsored by a foreign power, suggesting the team were operating on false documents.
Mr al-Mabhouh was a founder member of the Izzedine al-Qassam Brigades, and was thought to be behind the kidnap and murder of two Israeli soldiers in 1989 during the first Palestinian Intifada.
The Izzedine al-Qassam Brigades have been responsible for suicide bombings and rocket attacks across Israel.