Up to 25,000 new homes will be built by the end of next year, Taoiseach Micheál Martin has said.
Mr Martin said the Government's target is a "challenging" figure.
Around 12,750 will be social homes. Of those, 9,750 will be direct builds by approved housing bodies or local authorities.
The Covid-19 pandemic has had a big impact on this year's target, with around 18,000 new homes expected to be completed by the end of this month.
Mr Martin said that while the number of homeless people has dropped since March, the Government is giving "everything we can".
"We have pledged around €3.3bn for housing in 2021. The key issue will be capacity to deliver to get the houses built," he said.
"Covid has impacted in the first wave because in the first lockdown, construction shut down and that has impacted housebuilding."
Mr Martin said the Land and Development Agency Bill was approved by the Cabinet, which now puts the LDA on a statutory footing.
"That's a significant milestone. It is another weapon in our armoury," he added.
"The Housing Affordability plan also came through Cabinet, so the minister has been very active.
"There are very challenging issues in the context of both pieces of legislation.
"They will come into the Dáil and the Oireachtas in the new session.
"From July, we talked about voids, and through the July Stimulus we took 40 or 50 million euro to get 2,500 voids - houses in disrepair under local authorities - and get them done and we did.
"By the end of the year, the majority of those will be done.
"There's an energy come to this, and every morning when I wake up I say, 'What are my key priorities? Housing, health, climate change in addition to Covid and the education'."
The Taoiseach said the challenge will be post-Covid-19.
"There will be an impact in the lifetime of this Government," he added.
The Economic and Social Research Institute (ESRI) said 33,000 units every year are needed to keep up with the population.
"My worry is about getting to the 33,000 figure which the ESRI has said is necessary to put a dent into the waiting times," Mr Martin said.
"I'm not happy yet that we are where we should be and I think we'll keep driving it on.
"On homelessness, I think numbers are coming down, but we want to keep that down. Six thousand people exited homelessness last year.
"So we want to concentrate on getting more people out of homelessness."