Yorkshire Water confirmed they had received reports of people making phone calls claiming to be on behalf of Yorkshire Water saying that the boil first order had been lifted.
Residents in Thorne and Moorends reported receiving the calls.
A spokesman from Yorkshire Water said: "The order is still in place and will remain so throughout Monday."
Customers in 3,600 properties in Thorne can now use their tap water but MUST BOIL IT FIRST before drinking or cooking with it, Yorkshire
This position will remain the case throughout Monday, until further sample results are received.
A spokesman said: "Sample results on Sunday were encouraging but Yorkshire Water are being extra cautious and will not remove the boil first instruction until further samples confirm the water is once again fully safe to drink."
Charlie Haysom, the company’s Director of Service Delivery, added: “I am pleased that sample results are encouraging and that we may be able to restore normal service as soon as possible. However, we must emphasise that until we receive further sample results, water has to be boiled first before being used in cooking or for drinking.
“We acted swiftly once initial samples on Friday afternoon indicated the water was not safe to use for drinking or cooking at all. By Saturday lunchtime that had been downgraded to a boil first instruction and we hope full normal service may be restored as soon as possible.
“Yorkshire Water’s investigations as to the cause of the incident are ongoing and continue to focus on the Coulman Industrial Estate as a potential source of the problem.”
As part of the effort to restore normal service in the Thorne area work will be carrying out on a flushing procedure all day today.
It is possible customers in the area may notice some discolouration of their water whilst the flushing takes place - this poses no additional risk to customers.
Yorkshire Water has said that customers in Thorne may notice elevated levels of chlorine, which is used safely as part of normal water treatment processes. This slight increase in chlorine levels may result in the water having a slight odour, but it is safe to drink once boiled.
A collection point for water is available at Trinity Academy School, Thorne.