Tánaiste Micheál Martin has said the State is "without question turning the corner” in relation to the building of new houses.
According to figures from the Residential Tenancies Board released last week, thousands of people are going to face evictions in the coming months.
The RTB data showed 4,741 notices to quit were issued by landlords in the three months leading up to when the eviction ban was announced on October 28.
It also emerged the vast majority of landlords who issued notices to quit to their tenants did so because they wanted to sell their property.
This comes as the Government confirmed the eviction ban would not be extended beyond March 31 due to concerns that an extension would damage the supply of rental properties in the long term.
Mr Martin said the Government along with local authorities will do “everything we possibly can” to prevent people from becoming homeless.
He said the Government will develop a package of measures for the next budget to retain existing landlords and attract new people to the market.
“The key aspect to that is supply, we have to build more houses and build them more rapidly, but in the short term we will be leasing more housing, particularly social housing,” he told RTÉ’s Morning Ireland.
“We will also be expanding and have given directives to local authorities in respect of attaining tenants in situ where houses have been sold for local authorities to buy those houses.
“Thirdly, we will be looking at a new cost rental framework to govern situations where houses are being sold.”
Mr Martin said ultimately, more houses need to be built. He said 30,000 houses were built last year, with 9,000 in the last quarter.
“What I’m saying is we’re going to do everything we can to prevent people from becoming homeless,” he said.
“There are many factors leading to people becoming homeless and they’re wide and varied but the fundamental solution to this is more housing.”