Nineteen mobile water tankers have been deployed across Wales to supply thousands of homes with no supply.
About 3,000 properties in western Carmarthenshire have been hit by problems at a reservoir and 2,000 in Powys are also affected.
Dŵr Cymru Welsh Water said its engineers were working around the clock to restore services.
It said it was dealing with around 185 burst mains in a day, blaming record low temperatures followed by the thaw.
The main areas affected in Carmarthenshire include the postcodes SA31 and SA33 around St Clears.
The problem is expected to continue until at least Thursday.
Supplies to 2,000 properties in Llandrindod Wells (LD1) in Powys are also being hit by the weather but residents should start to see normal service Wednesday afternoon.
Dŵr Cymru Welsh Water began giving out bottled water to customers on Wednesday morning.
A spokesperson said several thousands customers were affected by the disruption to supplies around the country, with Carmarthenshire worst hit.
Operations director Peter Perry said the company was working at "full stretch".
"We are dealing with an unprecedented level of bursts not only on our system but also on the private supply side - on customers' own pipes," he said.
"Yesterday, we dealt with 250-plus bursts on our own system.
"I've been in the business for 30 years and the levels of bursts - we've never seen the like before," he told BBC Radio Wales.
"Our biggest incident is in south Carmarthenshire. There are about 3,000 properties without water. We are doing everything we can to get supplies restored.
"We've had a significant failure at a pumping station."
Elsewhere, there have been reports of water problems in Rhiw, Gwynedd, with customers without water or low pressure in the Llyn Peninsula (LL53).
There is a similar problem under investigation in Haverfordwest, Pembrokeshire, with staff taking calls from customers with no water or low pressure in the SA62 postcode area.
Meanwhile, a burst main has been repaired but continues to affect supplies to Miskin, near Cardiff, and Ynysybwl in Rhondda Cynon Taf while the system is "recharged".
Dŵr Cymru Welsh Water said it logged 5,000 calls from customers reporting problems on Boxing Day, compared with 50 on a typical busy day, and about 185 during a cold snap.
It is giving updates via its website to customers whose supplies are affected.