Taoiseach Micheál Martin has said the target is to bring the talks on the mica compensation scheme to a conclusion by the end of the month and that a proposal would come to Cabinet in early October.
Speaking to journalists in New York, Mr Martin said it is complex because there are different house sizes and a whole range of issues.
He said the aim is to establish a system to repair or rebuild houses much faster than was expected.
"The whole purpose of the talks is to get to a position whereby we can get houses repaired or rebuilt, whichever is the issue and a system to do it properly in a much faster timeline than might have been originally envisaged," he said.
The Taoiseach added that he does not want any hardship on the family and that "good progress" has been made.
"This Government is committed to enhancing the original scheme that was there," he said.
Mr Martin said the administration of the scheme is being looked at so that it speeds up the "timeline around this".
He commented that there is quite a substantial challenge in terms of the numbers involved, in terms of the danger, and also the fact that it is very unsatisfactory for the homeowners and their families to be living in accommodation where cracks are appearing.
Earlier, Minister for Public Expenditure and Reform Michael McGrath said a significant enhancement of the mica compensation scheme is likely to be agreed in weeks.
Mr McGrath said everything is on the table and the Government has not ruled out anything.
Meanwhile, the Tánaiste and Fine Gael Leader is to meet with some of his party's TDs on Friday who are calling for 100% compensation for those whose homes were built with defective blocks.
These include Donegal TD Joe McHugh, Clare TD Joe Carey and Alan Dillon from Mayo.
Leo Varadkar told a meeting of his party tonight that everything is on table and he is not opposed to a 100% scheme.
Several speakers at the meeting in Leinster House said there was an urgent need for such a scheme.
The meeting heard that this was a crucial period the revision of the current scheme and a final report on the matter will be completed before the end of the month.
Separately, Sinn Féin TD Pádraig Mac Lochlainn accused Mr Varadkar of yesterday lecturing families whose homes have been destroyed by mica.
"The families in the west of Ireland have been treated like second class citizens," he said.
The Donegal TD said the Tánaiste had uttered glib comments around the issue.
He said the human toll of this ordeal has been heartbreaking with many people experiencing unbearable mental stress.
"It is agonising to see your friends and family suffer in this way," said Mr MacLochlainn, who lives in Buncrana, which he said was at the epicentre of the problem.
Under questioning by @PadraigMacL, @mmcgrathtd tells the Dáil that the Govt "absolutely recognise the devastating consequences" for families who live in mica-affected homes. The Govt has "ruled out nothing" re compensation, he says | https://t.co/krP75G2Gjq pic.twitter.com/wJ0uxwy8vN— RTÉ News (@rtenews) September 22, 2021
In response, Minister McGrath said there is an appreciation in Government of the devastation caused by mica.
The working group looking at the issue will consider the submission from the householders affected.
He said Minister for Housing Darragh O'Brien will examine the group's report at the end of the month and then make a decision quickly around what is required.
The minister said things such as rent and storage costs are all on the table.
He added that he expects there will be a "significant enhancement" of the scheme agreed by Government.
Additional reporting Brian O'Donovan, Micheál Lehane