It said bad weather meant there was now more water in the chasm and that Welsh Water had had to stop work so a crane could be brought in to stabilise it.
Pumps trying to divert the river were struggling to cope, said the authority.
“As of this morning, the sinkhole has increased in size,” a spokesman said.
“Unfortunately, this means that we are no longer in a position to allow householders from the lower end of the cul-de-sac to return home safely, possibly until early next week.
“However, this timeline will be heavily reliant on weather conditions over the weekend.”
On Thursday night, a number of roads were closed – the A48 Severn Bridge between Wales and England because of strong winds, and the B4242 between Resolven and Aberdulais in Neath Port Talbot because of flooding.
The A48 between the Pyle and Porthcawl roundabouts in Bridgend county was also shut because of a fallen tree.
An amber warning for wind has been issued for parts of the UK with the arrival of the fourth named storm of the season.
Storm Darragh is expected to bring gusts of up to 80mph (128km/h) late on Friday and into Saturday.
The warning for “potentially damaging” winds is in place for the west coast of the UK from South Ayrshire in Scotland, through Wales and down to Cornwall, as well as in Northern Ireland.
It is in place on Saturday from 03:00 GMT until 21:00.
On Thursday, the Met Office issued yellow weather warnings for rain and wind that covered Wales and other parts of the UK.
Natural Resources Wales currently has a number of flood warnings and alerts in place.
