Sinn Fein has called on the Government to implement the temporary eviction ban this week.
Party leader Mary Lou McDonald told the Dail she is “anxious” to assist the Government to ensure there is no delay in the winter ban becoming law.
The Government approved a one-off ban on evictions for the winter period during Tuesday’s Cabinet meeting.
Under the plans, notices of termination can be issued to tenants but the property does not have to be vacated until the ban is phased out next year, with the last date on June 18.
The Government is hoping to bring in the ban from November 1 after new legislation is introduced next week.
Ms McDonald told the Dail there are concerns that the ban may not be introduced until December, which would be “far too late”.
“A delay like that would result in hundreds more adults and children being forced into homelessness,” she said.
“But if we work together, we can get the right legislation and we can get it passed very, very quickly to prevent this from happening.
She added: “You have moved on this matter of a ban on evictions. You say that you will bring it forward with all due haste.
“Can I say we are anxious to assist you in that?
“Can I suggest that we get this work done this week?
“Get let’s get this done this week, publish the legislation, work with the opposition, work with us constructively and let’s get this done this week because families as we speak and as we meet here are desperate are terrified at the prospect of losing fair rented at home.”
The Taoiseach described the ban as “positive and necessary”.
He said if approved in the Houses of the Oireachtas it could take effect from the beginning of November.
“We are in very, very unprecedented circumstances,” Mr Martin said.
“The decision of the government this morning in relation to the eviction ban, I think is a positive and necessary.”
Labour leader Ivana Bacik welcomed the Government’s “u-turn” on the temporary ban on evictions of rental properties.
But she said it will come too late for the 11,000 people including 3,220 children who are currently homeless.
“We know that these figures will only continue to grow after the eviction ban has concluded unless we address the core problem of a lack of social and affordable homes,” Ms Bacik said.