About 600 homeless families remain in emergency hotel or B&B accommodation six weeks out from a deadline to end the practice.
The promise to stop using the hospitality sector for long-term stays for parents and their children was made last July by Housing Minister Simon Coveney.
About 39 million euro was spent booking bedrooms for the homeless in guest houses, B&Bs and hotels in Dublin in 2016 - more than double the cost of the previous year.
Taoiseach Enda Kenny said it is a challenge to meet the looming deadline.
But he added: "My information from the Housing Department is that you will see a very substantial drop in that by the end of June.
"It's always a very difficult challenge to meet because it's been exceptionally ambitious, but they are really focused on moving this along here now."
The Dail was also told that there are 28,000 vacant homes in the Dublin suburbs, including 750 in the Finglas area alone.
Mr Coveney recommitted last month to meet his July deadline to end the use of hotels for the homeless as official figures revealed that 3,299 adults and 2,134 children were homeless.
He said the practice would stop unless the circumstances are exceptional.
Joan Collins, Independents 4 Change TD, dismissed the Government's claims.
"This target will not be reached despite the minister's most recent assurances," she said.
Ms Collins said the Government's initiative to create 10 hubs in Dublin to deal with the homeless crisis would not be ready by July 1, and she claimed they are a form of "temporary emergency accommodation".
"Moving families from one form of temporary emergency to another form of temporary emergency accommodation often miles away from schools their children attend is not a solution," she said.
Focus Ireland said it was concerned the Government's plans for "family hubs" for homeless parents and their children will become a long-term accommodation.
Spokesman for the charity Roughan Mac Namara said: "Focus Ireland does not believe whether the minister meets the deadline to end the use of commercial hotels is the key issue in terms of tackling and ending this crisis.
"The deadline we are most interested in is for the minister, and the Government as a whole, to set a clear deadline that no family will be allowed to remain homeless for longer than six month after losing their homes.
"We need to make sure the drive and focus is firmly on securing long-term homes for families and any individuals who are homeless."
Focus Ireland pointed to the most recent Government figures on homelessness which recorded 7,472 people homeless in Ireland.