Tánaiste Joan Burton has expressed her sympathy on behalf of the Government to the family and friends of Karen Buckley.
Speaking in the Dáil, Ms Burton expressed particular sympathy with Ms Buckley's parents John and Marian and her brothers.
She said: "It's every parent's nightmare what has unfolded in the past few days."
The Tánaiste added that Minister for Foreign Affairs Charlie Flanagan, Minister of State Sean Sherlock and the Consulate office in Scotland are doing everything they can for the family.
Her sentiments were echoed by Sinn Féin's Mary Lou McDonald and Fianna Fáil's Éamon Ó Cuív.
Mr Flanagan earlier expressed his sympathies to Ms Buckley's family after police searching for the missing student found remains on a farm near Glasgow.
He said he was greatly saddened by the news emerging from Scotland.
"All of our thoughts and prayers are with Karen's parents, John and Marian, and with all of her family and friends at this tragic time."
The Glasgow Caledonian University released a statement saying the university community was deeply saddened by the news.
The 24-year-old, who had worked as a nurse, began studying occupational therapy at the university in February.
The university said thoughts are with Ms Buckley's family, friends and classmates at this very difficult time.
Support services have been made available for students.
Ms Buckley had previously studied nursing at the University of Limerick and it also expressed its sadness about the developments.
It said: "Karen was a very valued member of the UL Community as well as the wider nursing and medical communities in Limerick, having spent time working in both the University Hospital Limerick and the University Maternity Hospital.
"The thoughts of the entire UL community are with her parents and family and her wide circle of friends as well as her UL classmates and medical colleagues."
Meanwhile, a fundraising page for Ms Buckley's family has raised more than £40,000 (€55,000) since it was set up yesterday.
More than 2,000 people have so far donated to the 'Help Find Karen' gofundme.com page, many of them anonymous.
The page, which had an initial target of £5,000, will close at 9.30pm tonight.
It was set up by Ms Buckley's University of Limerick classmates "in the hope of raising funds to help Karen's family in any way possible during this difficult time".
The funds will be used to pay for the family's accommodation and travel expenses, and for the upkeep of their farm in Cork.
This morning, police in Glasgow searching for Ms Buckley discovered human remains on a farm north of the city.
This afternoon they confirmed that the body was that of Ms Buckley.
A 21-year-old man has been arrested in connection with her death.
Ms Buckley, from Mourneabbey near Mallow in Co Cork, moved to Glasgow earlier this year.
The local community and people elsewhere have been responding to the developments in Scotland.
A special prayer service was arranged in Ms Buckley's home village in north Cork last night for people to show support for the family.
The Mass of Hope was held at the Church of St Michael the Archangel in Mourneabbey.
Bishop of Cloyne William Crean led the prayers.
"On my own behalf and on behalf of the faithful of the Diocese of Cloyne, I wish to offer prayerful support to the family of Karen Buckley at this painful time as they await the safe return of Karen," he said.
Mourneabbey Community Council has said its thoughts and prayers are with the Buckley family.