Two hundred people this evening gathered outside Leinster House for a vigil in memory of John Corrie, who was found dead in a nearby doorway on Molesworth Street yesterday morning.
Bouquets of flowers were also left on the spot where the homeless man's body was found.
A post-mortem examination on the Kilkenny man is to be carried out tomorrow or Thursday.
Taoiseach Enda Kenny has said the Dáil will debate the homeless situation next Tuesday.
He said the death of Mr Corrie, 43, was most distressing.
However, pressed by Opposition leaders, Mr Kenny said that homelessness was often a complicated situation and raising the rent allowance was not the answer.
Fianna Fáil leader Micheál Martin said the Government had failed to come to grips with the homelessness crisis.
He said there were 168 adults on the street and 800 children in emergency accommodation and hotel rooms.
He asked why Mr Kenny had not heeded the agencies dealing with it and raised rent allowances.
Mr Kenny said homelessness was often a complicated situation.
The money provided to NGOs to deal with homelessness was significant to say the least, he said, and added that raising the allowance ran the risk of fuelling rent inflation.
The answer to the problem was, as he put it, houses, houses, houses.
Sinn Féin leader Gerry Adams said there should be an emergency intervention.
However, Mr Kenny said €55m had been set aside to deal with the homeless and a huge social housing programme initiated.
Independent TD Catherine Murphy asked when the Taoiseach would show the same outrage over homelessness that he did over allegations about a nursing home in his own constituency.
Meanwhile, Minister for the Environment Alan Kelly has called together the capital's local authorities and housing charities for a summit on homelessness on Thursday.
The move follows a call for urgent talks on the crisis by Dublin's Catholic Archbishop Diarmuid Martin, who has also offered church property to shelter 40 long-term homeless people.
Mr Kelly said he is not convinced the issue in relation to homelessness is about funding and said that there needs to be more joined-up thinking on the issue.
The minister said the ambition of the Government was still to solve long-term homelessness by 2016.
There are 1,500 emergency units and 140 new units will be made available in the coming weeks, he said.
He also said 640 units of accommodation across Dublin that are boarded up will be opened up.
The minister said: "I want to meet with elected mayors, CEOs of the local authorities and representatives of the voluntary organisations to address the serious challenges posed by homelessness in the Dublin region.
"I want to focus attention and activity on this issue which is very important at any time but is particularly sensitive at this time of year."
Woman tells of shock of finding body
The woman who discovered Mr Corrie's body said she became concerned about him because he looked to be lying in an awkward position on the ground.
Speaking to Ryan Tubridy on 2fm this morning, Sophie Pigot said that when she checked the man's pulse he was "ice cold" and she then realised that the man was not alive.
Ms Pigot alerted the garda on duty at Leinster House, who called an ambulance.
She said she then went to Buswell's Hotel across the road and got a white sheet to cover the man.
Ms Pigot said she was extremely sad and shocked that something like this could happen in Ireland.
She said she could not sleep last night thinking that it was 24 days to Christmas and many people in Ireland are living on the streets.
Ms Pigot said that people should notice a homeless person at the ATM this Christmas and realise that they are a person.
A friend of Mr Corrie has said a lot more could have been done to save his life.
Derek Buchan, who is also sleeping rough, blames his friend's death on the scarcity of emergency overnight accommodation in the capital city.
He told RTÉ News that the bed-shortage becomes evident each afternoon when homeless men and women call the four local authorities' freephone number to make a reservation.
He said you could be placed 50th in the queue while you are left waiting on phone.
However, tonight the State said the voluntary services it funds made a significant number of interventions with the late Mr Corrie, citing holistic and assertive on-street assistance and repeated offers of emergency beds.
The Dublin Homeless Regional Executive said that, as was his right, Mr Corrie did not accept these beds.
The executive extended its condolences to Mr Corrie, his family and friends.
Mr Buchan said he last saw Mr Corrie three days ago when they shared a bottle of rum.
Dublin 'deeply divided', says Archbishop
Dr Martin earlier described the capital as "deeply divided".
He said he was "very deeply concerned about a deeply divided Dublin where on the one hand there is rejoicing at increased spending over the Christmas period and on the other hand where the number of those homeless and hungry is actually increasing".
Speaking on RTÉ's Morning Ireland, he said he would hate that the death of this man would be a one-day outrage.
Dublin Lord Mayor Christy Burke earlier said he was willing to host and facilitate a homeless summit.
Brother Kevin Crowley of the Capuchin Day Centre in Dublin said he does not see why people who are sleeping rough cannot be given accommodation in the short-term.
He appealed to the Government to take homeless people off the streets, particularly in the run-up to Christmas.
Speaking on RTÉ’s Morning Ireland, Brother Kevin said there was no point in allocating money to organisations to give homeless people accommodation when there was no accommodation specifically available to them.
He said: "There's so many places vacant, so many different apartments around the city, why not use those up and give the people dignity.
"Some of these people that I meet, the mothers and children, they leave those rooms at nine o'clock and they are walking the streets until eight in the evening time. That is no way to have respect for our children," Brother Kevin said.
Meanwhile, Minister for Public Expenditure and Reform Brendan Howlin has said the death of Mr Corrie was beyond tragic and was a horror.
He said there is an urgent crisis in relation to people sleeping on the streets and he would embrace any ideas coming from the Archbishop of Dublin or anyone else to ensure that there was not another tragedy.
Also speaking on RTÉ's Morning Ireland, Minister for Agriculture Simon Coveney said the main problem is the lack of houses.
There had effectively been no houses built over the last five or six years in Ireland and he said this had to change.
The Government announced a €3.8bn housing commitment last week, he said, which will build 18,000 houses before the end of 2017.