The couple had travelled to the Mansion House in Dublin where a book of condolence was opened by lord mayor Críona Ní Dhálaigh.
The President and his wife passed a queue of people, young and old, waiting outside the Dawson St landmark, to sign the book on behalf of the Irish people.
Mr Higgins said he believed the whole country had been deeply moved by the tragedy.
“I am glad I had an opportunity to sign the book at the Mansion House. I know there are many other books being opened in different places and the queue outside makes its own expression of the anxiety of the public to express their sympathy with the families,” he said.
Ms Ní Dhálaigh said she had called for a fire safety audit of all halting sites managed by Dublin City Council in the wake of the tragedy.
“This can never happen again and we need to make sure our own halting sites are actually safe,” she said.
The Lord Mayor said she was sure other local authorities throughout the country would also want to assess the safety of their sites.
Among those queuing outside was Katherine Byrne, a teacher from the Holy Child Community School in Sallynoggin, Co Dublin. “Our school is not that far from Carrickmines and we have a number of pupils who are members of the Traveller community,” she said.
Lucia Tijeiro, who grew up in Spain but now living in Ireland, said she wanted to show her support and to pray for the people who died.
Mary McHugh from Dublin said she knew her expression of sympathy was not going to make any practical difference — it was just a tiny gesture.
“But, who knows, maybe in a calmer time, the families affected will realise, out there in the anonymous world, people are feeling sorry for them,” she said.
Also in the queue was, Willie van der Westhuizen, a diplomat from the South African embassy, who arrived to express the condolences of the South African government.
Meanwhile, messages of condolences over the Carrickmines tragedy, and the shooting of Garda Anthony Golden in Louth on Sunday, will be heard in the Dáil at 2pm today.
Taoiseach Enda Kenny and opposition leaders will express the country’s sorrow over the incidents before Finance Minister Michael Noonan’s budget speech at 2.15pm.