A statement from the First and Deputy First Ministers, which followed talks at Stormont with officials from NI Water, said the agency's response to the situation had been "clearly inadequate".
An emergency meeting of the Executive has been called for Thursday.
The Deputy First Minister said the people of Northern Ireland have been "badly let down" by how the problem has been handled, calling it a "grave crisis within NI Water".
"It's not good enough, and we are as angry as anyone else about the situation that has been inflicted over these past few days," Mr McGuinness said.
"We have also spoken to the Scottish First Minister Alex Salmond and have accepted an offer of 160,000 litres of water which should be here today.
"We must face up to the reality that the effort was not good enough, but the focus has to be on those who were badly let down, to help them see that a real effort is being made to improve the situation."
Officials from NI Water have apologised for how the situation has been handled, admitting that the organisation was "caught on the hop".
"I am very, very sorry for people being off supply," Chief Executive Laurence MacKenzie said. "My focus now is on getting back on."
Interim Chairman Padraig White added: "The call centre has been overwhelmed. I don't think the response of the organisation has been satisfactory, particularly in terms of conveying information to people."
Some 36,000 people across Northern Ireland continue to struggle without water, and many have been experiencing the drought since before Christmas.
NI Water, the government agency in charge of the region's water, has taken thousands of emergency calls since the thaw began earlier this month.
Efforts have been made to circulate water supplies around the system in a bid to provide some relief to all areas of Northern Ireland, but customers have complained that they were not told when their water would be switched off, or when it would be returned.
From 4pm on Wednesday, NI Water said it will be launching a "revamped" version of its website, containing information on which areas are affected and where public water tank depots can be located.
In a statement, the company said over 95% of all customers are back on supply, and the supply of water to customers has been pushed to the highest level ever - up 40% to 850m litres per day.
There have however been warnings that interruptions will continue over the next few days as dwindling reservior stocks are refilled.
A new emergency hotline has been set up by Belfast City Council, and can be reached on 0800 707 6965.
Castlereagh Borough Council has been making further supplies of water available from 9am from its Civic Offices at Bradford Court, opposite the Forestside Shopping Centre. The council's incident line telephone numbers are 028 9049 4662 and 028 9049 4663.
The Olympia Centre on the Boucher Road will be providing mains water from 8pm to 10pm, and police are asking motorists to avoid the area between the Broadway roundabout and Stockmans Lane to allow people to park along the roadside.
Another depot has now opened at the Lisburn Omniplex, and mains water is available at leisure centres across Newtownabbey.
In Co Fermanagh, water for domestic usage can be collected from the Fermanagh Lakeland Forum in Enniskillen, Bawnacre Centre in Irvinestown and Castlepark Centre, Lisnaskea. The venues will be open until 9pm on Wednesday, and from 10am to 10.30pm on Thursday.
Residents can take 20 litres but must bring containers, and are advised to boil the water before use.
A number of venues are also being opened up for showering free facilities.
In the Bann area, showers at the Banbridge Leisure Centre and Dromore Community Centre can be used between 9am and 8pm for the rest of the week.
The Valley Leisure Centre and at Sixmile Leisure Centre in Newtownabbey are also open.
The Public Health Agency has been giving advice for safe use of water when mains supplies are not available.
They say water should be used for hand hygiene when preparing food, rather than for showering - rain water can be collected for flushing toilets. Any water taken from depots should be boiled before drinking.