The kidnappings, thought to have been carried out by al-Qaeda terrorists from Mali, happened during an attack on a BP gas field at about 5am GMT on Wednesday morning.
French troops are in Mali, which borders south Algeria, preparing to launch an attack on Islamic militants.
While the man, who is originally from Andersonstown in west Belfast, is understood not to have been hurt during the abductions, reports indicate that two security guards - thought to be British and French - have been killed.
"I can tell you he did make contact with members of his family this morning," UTV reporter Judith Hill, who has been following the story, said.
"First of all to re-assure them he is okay and not being mistreated. I understand he also told his loved ones he was being held by al-Qaida.
"Obviously, his entire family - including his wife - are distraught."
The man, who is travelling on an Irish passport, is married with children - he cannot be identified at this stage, due to the delicate nature of the hostage situation.
The Government stands ready to use all the resources available to us to ensure that our citizen is released as soon as possible.
Tánaiste Eamon Gilmore
A spokesperson from BP said the site in the eastern central region of Algeria was attacked "by a group of unidentified armed people".
The spokesperson added: "Contact with the site is extremely difficult, but we understand that armed individuals are still occupying the In Amenas operations site.
"Algerian authorities are engaged with the incident - UK authorities have also been advised."
An emergency response system has been activated by BP and the firm has also set up a helpline for relatives of those affected.
The gas field is operated jointly by BP/Statoil and Sonatrach, the Algerian state company.
Tánaiste Eamon Gilmore has called for the immediate release of the local man.
"The Consular Assistance unit in the Department is providing consular assistance to the family and are in close contact with its international partners, and a wide range of other contacts, in order to establish the facts of the situation," he said.
"At this stage, the identity and motives of the kidnappers is unknown ... I would ask that the family be allowed privacy at this difficult time."
Sinn Féin President Gerry Adams said: "I have been in touch with the family to express my solidarity at this difficult time and I have spoken with the Irish government's Department of Foreign Affairs who are doing all they can to help the family and secure the release of the kidnapped Irish citizen.
"I would appeal to the kidnappers to release their victim and all of his colleagues."
Meanwhile, Prime Minister David Cameron chaired a 45-minute meeting of Whitehall's Cobra emergency committee, at which ministers were updated on the developing situation.
Afterwards, Mr Cameron's official spokesman said: "The ongoing incident has involved various nationalities, including several British nationals.
"We are working with BP to support the families of staff and provide consular assistance."