Taoiseach Simon Harris has said a multi-agency meeting is taking place to discuss the growing number of tents on Dublin's Grand Canal.
"What happened on Mount Street was allowed to go on for weeks and weeks, and months and months in fact, this will not be the situation in relation to the Grand Canal," Mr Harris said.
The Taoiseach said he is standing by his "clear commitments in relation to not wanting to see another Mount Street situation develop" and said work is ongoing to find accommodation.
"I am confident that more progress on accommodation will be made in the hours and days ahead," Mr Harris added.
There are around 80 tents pitched along the Grand Canal, after more than 100 tents were moved from around the International Protection Office on Mount Street last week.
Speaking on RTÉ's Drivetime, founder and chair of the Tiglin charity, Aubrey McCarthy, said the number at the Grand Canal is rising.
"These are new arrivals, when you look at the figures there are over 400 arriving every week," Mr McCarthy said.
"Mount Street is just one week of asylum seekers arriving into Ireland."
This morning many on the Grand Canal were getting ready to walk the short distance to the International Protection Office to find out if there was any update on their situation when the office opened.
They are among 1,710 male asylum seekers without an offer of State accommodation, according to the Department of Integration.
Some of the International Protection applicants sleeping in tents by the canal say they feel vulnerable as they wait for safer and more suitable accommodation to be provided.
One man told RTÉ News that he did not stay in his tent last night as he had heard about possible threats from anti-immigration campaigners.
He said he knew there was a protest happening yesterday and he feared what might happen so he hid in McDonald's and on the streets until the early hours saying he "felt safer".
Many of the men in tents praised the work of volunteers who have been making sure they receive enough food and to help them seek medical attention if they require it.
Volunteers say that authorities are also working around the clock to provide support but they say that they also believe "a broken system" is partly to blame for the high numbers seeking asylum.
Volunteer Olivia Headon said while many of the people seeking asylum are fleeing war or persecution others who are not coming from a conflict zone cannot get a visa to work here and so they choose to go through the International Protection route instead.
There are calls locally for a garda presence at night to ensure that those having to sleep outdoors can feel safe.
New accommodation expected this week
Many of the people seeking refuge at the Grand Canal are from Afghanistan, with one man saying he came to Ireland after passing through the UK first.
Others seeking International Protection are from Nigeria, South Africa, Pakistan and other parts of the Middle East.
One man from Nigeria said he did not expect to arrive to Ireland and be in a tent, but said he feels safer than if he was in his native country.
He said he understands the difficulties for the Government with large numbers arriving, but is hopeful that accommodation will be secured for them soon.
Most of those sleeping in the tents say they are staying warm, but are having to walk 30 minutes to access toilet and shower facilities.
Read More: Mount Street shifts focus onto Ireland's migration policy
New offers of accommodation are expected to come on stream this week and it is understood that additional capacity has been identified to assist asylum seekers who currently do not have a place to stay.
However it is unclear how many places will be made available this week; where they are located; and how the asylum seekers will be contacted.
In tandem, the Government is understood to be focusing on acquiring State-owned land in order to set-up tented accommodation for future arrivals.
This is expected to take a number of weeks to complete in order to ensure that adequate facilities are on the new sites.
Mr Harris has already convened a multi-agency and multi-departmental group to overcome any logistical problems.
The reappearance of tents close to Mount Street is politically sensitive, given that Mr Harris told the Dáil last week that what he called "makeshift shanty towns" would not be allowed to develop again.
Minister for Agriculture Charlie McConalogue said that Ireland has seen record numbers seeking international protection in the last two or three months which has put pressure on the system.
Speaking on RTÉ's Today with Colm Ó Mongáin, Mr McConalogue said that this year Ireland had sourced 4,000 accommodation places for asylum seekers, and that the Government is working intensely to source additional accommodation.
"The focus for the moment will be on sourcing State land where tented accommodation can be provided or State-owned buildings - that work is ongoing," he said.
He added that with more people coming every week it has put pressure on the situation when there has been limited places given.
Call for 'coherent and centrally coordinated plan'
Labour Party leader Ivana Bacik said she is very disappointed by the number of people with no option but to sleep in tents.
Speaking to RTÉ News, she said it is inhumane and also raised concerns for their safety particularly with the "far right on march around Dublin".
She said there is a need for a coherent and centrally coordinated plan from Government and she said there are empty state-owned sites within a stones throw of the canal.
She said volunteers have been doing so much to help those coming here seeking refuge.
Ms Bacik also said that for months her party and others have been pointing out that Minister for Integration Roderic O'Gorman's department should not be shouldering all of this responsibility.
Local residents and workers in the area by the canal have described the ongoing issue of people in tents while they await offers of accommodation as difficult and "tricky".
Many are also critical of the Government's response to date.
They said the situation is not fair for either those seeking refuge or those with tents on their doorstep.
One resident, Gerry McKeowan, said he hopes that the tents being so visible again may instigate some better and swifter action from Government.
Green Party Councillor Hazel Chu said she fully understands people's concerns.
She said she hopes Government collaboration across departments will continue to address this emergency.
She said everyone is concerned by this issue and residents are worried for the individuals in tents and want to make sure they are safe.
Additional reporting Paul Cunningham and Dyane Conor
