The Northern Ireland Housing Executive (NIHE) has said it has faced "unprecedented and record-breaking levels" of people seeking emergency accommodation.
It said more than 4,500 households availed of emergency temporary accommodation over the weekend.
NIHE added that additional crash bed facilities were also made available on Saturday.
"We always strive to ensure that everyone presenting to us is cared for," a statement said.
The People's Kitchen, a Belfast-based charity which supports homeless and vulnerable people, was critical of the NIHE's response.
The charity's founder and Belfast city councillor Paul McCusker said that a "high amount" of those presenting for support have no option but to sleep rough.
"[The] Northern Ireland Housing Executive advising there is nothing available, even though they have a legal duty," he said in a statement.
"We cannot highlight enough the seriousness of the situation on the streets of Belfast, a system by the Northern Ireland Housing Executive that is not fit for purpose for the most vulnerable men and women on our streets.
"This is an emergency".
However, the NIHE has refuted this claim.
A spokesperson said: "We do not accept that we failed any legal duty to homeless presenters this week."
"[On Saturday] we faced unprecedented and record-breaking levels of people presenting to us seeking emergency temporary accommodation."
The NIHE added severe flooding caused by hours of heavy rainfall following Storm Bert meant resources were "extremely stretched".
“Immense pressure was placed on the limited availability of temporary accommodation as a result of this week’s extreme weather conditions."
The NIHE said its teams were "active, on the ground, at a number of locations" over the weekend.
“Seventy-six people presented themselves to the Housing Executive’s out-of-hours service during Saturday. This figure would normally be around 20.
"We know that at least four of the 76 were as a direct result of the flooding”.
The NIHE added that around 11,000 households have benefited from emergency temporary accommodation over the last year.
"We will continue to assist the most vulnerable in our community as we have done consistently," the spokesperson added.
According to the DfC, the NIHE has two main duties in terms of accommodation.
The first - the interim duty to accommodate - means that if a person is homeless and has a priority need, they can be housed after their circumstances are fully investigated.
The second, applied to those who meet the four legislative homelessness tests as laid out in the Northern Ireland Housing Order 1988, including: eligibility, homelessness, priority need and intentionality.
More than 30,000 households are currently registered as being homeless, according to NIHE figures, while the latest Stormont figures show that more than £34m was spent on temporary accommodation in Northern Ireland in the last financial year.
Providing more social, affordable, and sustainable housing is among the key priorities in the Stormont Executive's draft programme for government.
Campaigners are set to meet the Department for Communities (DfC), which sponsors the NIHE, on Monday.
They said they will try to secure additional emergency beds for the winter.