Louth County Council has opened a book of condolence for Private Seán Rooney at County Hall.
The 24-year-old, originally from Dundalk, was killed on Wednesday night when the vehicle he was travelling in was attacked in Lebanon.
Flags have been flying at half-mast at military barracks around the country as a mark of respect.
Those who knew and served alongside Private Rooney have also been laying flowers outside Aiken Barracks in Dundalk.
Defence Minister Simon Coveney and the Defence Forces Chief of Staff Seán Clancy met with Private Rooney's mother and grandparents earlier.
The Mayor of Dundalk, Kevin Meenan, said the 24-year-old was very popular in the town.
"I would image there'll be people queuing up to sign it once it's out there," he said.
"It has really, really resonated with people here in Dundalk.
"The fact [of] his age, very, very popular, very well got and the tragic circumstances that it happened in.
"The fact that it happened so close to Christmas as well has really had a devastating effect on the town," he added.
'Good wishes and prayers'
Another soldier, Private Shane Kearney, was seriously injured in the same attack.
Fr Derek Ryan from the Holy Family Church in Dundalk has been supporting the Rooney family.
"The family would like to send a message of good wishes and prayers to the Kearney family down in Cork," he said.
"The family are very conscious of the amount of people that attended the vigil last night.
"They want to send their good wishes and they want to send their prayers to the Kearney family and to Shane in his recovery process," he added.