Northern Ireland Water has said it expects most homes in NI to have their water restored by the middle of next week.
It followed a three hour meeting of the organisation's board on Friday to discuss the recent crisis.
Four thousand three hundred and sixty homes remain without running water.
NI Water has said that about 20,000 properties will have an on/off supply, all of them in the east of Northern Ireland.
Northern Ireland Water's interim chairman, Padraic White, said that reservoirs in the region were "gradually refilling", but that they were still at a low level and that Belfast reservoirs were in the "most precarious position".
Mr White said the main areas of concern were "Greater Belfast and parts of Cookstown".
He said that he expected that by the middle of next week the number of homes affected in Northern Ireland would be in "the hundreds" and confined to isolated areas.
Mr White said the organisation was "sending record levels of water in to the network and water production is at its maximum capacity".
He also said it was a "normal part of water management" to put people "on a rotation of supply".
"We expect by mid-next week that it will no longer be necessary to put customers on a rotation basis," Mr White added.
"There may still be a tiny number, probably in the hundreds of those in more isolated places, who are very high up, who we are seeking to get supplies to."
Mr White acknowledged the organisation's emergency plan to deal with the water crisis had been "inadequate".
He also stressed the importance of householders and businesses fixing leaks on their premises.
He said the bursting of pipes at three premises in Newtownabbey, Belfast and Limavady had accounted for the loss of "10m litres of water per day".
Earlier, former Northern Ireland Water (NIW) acting chief executive Christopher Mellor, who was sacked in March, had described the water crisis as a "disaster waiting to happen".
"I think this is what happens when you get rid of the directors at the top of NIW, who knew what they were doing, and replace them with people who have no experience of running a water utility.
"In my view, the politicians, as well as the company, must take some share of the blame."
Mr White said he was amused at Mr Mellor's comments and said the emergency plan which had been in place was "developed under his stewardship".
Conor Murphy, the minister with responsibility for NI Water, said he was "entirely correct" to sack the previous board.
"I would have been rightly criticised for leaving the board in place, on the basis that Chris Mellor alone had some experience in a water utility company, given the procurement practices that were going on," he said.
After meeting with the board of NI Water on Friday, he said the Stormont Executive's focus was to get those suffering loss of water supply reconnected and to ensure there was no recurrence of the problem "for the rest of the winter".
He said he intended to announce "early next week" who would be conducting the review into the water crisis on behalf of the NI executive, as well as its time frame and terms of reference.
NI Water spokesman Liam Mulholland said on Friday its sole focus was to get customers back on supply.
"There will be a review and there will be lessons we will take from this and try and improve things going forward," he added.
An emergency session of the NI executive was held on Thursday to discuss the problems affecting the water supply, after which First Minister Peter Robinson called NI Water's response "shambolic" and "ineffective".
Deputy First Minister Martin McGuinness said NI Water's performance had been "totally unacceptable behaviour by an arms-length body".
The Royal Victoria Hospital, South Tyrone Hospital, Dungannon, and Lagan Valley Hospital, Lisburn, have been affected by the water supply crisis.
The Northern Ireland Secretary of State has warned there could be major changes in how the NI water supply is financed.
Owen Paterson said Northern Ireland's infrastructure had suffered over the years and that changes were now needed.
Eighty villages and towns were affected as pipes burst in the thaw.
The Scottish government is sending further supplies of water to Northern Ireland. Five lorry loads of bottled water are being delivered on Friday, with another two lorries scheduled for Saturday.
NI Water, a state-owned company, which is the sole provider of water and sewerage services in Northern Ireland, said an unprecedented number of leaks caused by the thaw following the long period of freezing weather had been putting "big pressure" on its systems.
The thaw followed the worst snow in Northern Ireland in 25 years and record cold temperatures.
As temperatures rose, burst pipes drained reservoirs, forcing NI Water to turn off the tap to the 80 locations.
Local councils are working to supply water and offer free showers to people without a mains supply and information is being provided on the NI Water website.