Environment minister Edwin Poots said some 34,000 homes were still without water, describing the problem today as "fairly significant".
He said engineers have restored water to 15,000 of the 40,000 homes without water but the thaw meant another 9,000 properties lost their supply.
Mr Poots said there had been a £3 billion investment project in recent years but the problem was a "historic issue".
But, he said, Northern Ireland Water and not the Government was to blame.
The minister told BBC Radio 4's Today programme: "The buck stops with Northern Ireland Water. It's a Government-owned company but it has its own board and the chief executive is beholden to the board so Northern Ireland Water is quite distinct in that it isn't run by the Government but nonetheless is owned by the Government."
He added: "The under-investment that took place was over the period of direct rule. A lot of that was really down to the Troubles, when money was diverted from areas such as water to pay for bombs and security services and so forth. But if you have 30 years of under-investment, you are not going to catch up in four or five."
Mr Poots said the Executive would not be putting up water rates for continued investment to improve the water network.
He said: "That will be a matter for the Executive to discuss and come to an agreement on. At this point it is not the intention of the Executive to introduce additional water charges."
An emergency meeting of the Northern Ireland Executive of ministers is being held today at Stormont.
Deputy First Minister Martin McGuinness and First Minister Peter Robinson have criticised NIW's performance.
Scotland has donated thousands of litres of bottled water as many households have been without water for days. Thawing conditions following the severe cold spell were initially linked to the bursts but now attention is turning to the history of under-investment in the water pipes.
NIW has been engaged in an extensive programme of capital works but the entire government at Stormont faces spending cuts.
Northern Ireland Secretary Owen Paterson has pledged the coalition's support but the issue of domestic water charging, opposed by most of the local parties, could be revisited.
Mr Paterson told Sky News he had "made it quite clear" to Northern Ireland ministers that "the British Government is ready to help in any way it can".
He said: "I had several conversations yesterday with Caroline Spelman, the Secretary of State for Defra, and we came up with various ideas which we're happy to help with."
As well as supplying extra tankers, he said the British Government could also help with information systems, because it had not been clear to people whether the water supply was switched on or off, and Defra has experience in crisis management.
He said: "The information has not been clear to people.
"They've had difficulty getting through on phone lines, they've had difficulty getting through on the internet, and, of course, some elderly and disabled people don't have access to the internet, so there has been a problem with communication."
Mr Patterson urged people to check for leaks around their homes, as the most of the leaks are around private property.
He said: "The simplest practical help that every single person in Northern Ireland could give is to go all round their property, literally in the next half hour, and check for leaks."
The Irish Republic has also suffered problems with its water supply.
Mayor of Drogheda Paul Bell has called on Louth County Council to consider assisting those in counties Down and Armagh.
Mr Bell said: "While we have had serious issues with water supply in County Louth, our engineers and outdoor staff have managed to stabilise the situation and address the majority of water leaks and burst mains over the past six days throughout the county.
"With our situation having improved, I have called on Louth County to enter into dialogue with the Northern Ireland water authority in order to assess what assistance, if any, we can give as a neighbouring local authority and as human beings to the citizens of Newry, County Down and Armagh."
'DREADFUL' FOR RESIDENTS WITH NO WATER
Frustrated residents have been forming long queues at emergency water points as the wait for water continues.
Phillip Dempster, 31, from south Belfast, has been suffering from interrupted supplies since the thaw began just after Christmas Day.
"It is just terrible, having to queue for water, it just should not happen," he said.
"I have young children at home with the school holidays, it is just dreadful."
He was at Avoniel Leisure Centre in east Belfast yesterday obtaining emergency supplies. The Scottish Government has given thousands of litres of bottled water.
With reservoir levels low and many pipe bursts not yet fixed, it could be some time before the problem is resolved.
Mr Dempster, an engineer, added: "I was looking forward to a nice relaxed Christmas break. Now I cannot even have a shower. It is just a disgrace and those up at Stormont should be ashamed of themselves."
If you suspect a burst water main, contact NI Waterline on 0845 744 0088.
Belfast residents can call the council’s emergency helpline on 0800 707 6965.