Messages bearing the company logo ask for for small payments to ensure letters or parcels are delivered.
One of the scams asks for a payment towards shipping costs, at a time when there has been confusion over deliveries to NI.
Royal Mail said it was aware of the issue and that fraudsters would invent “new and creative” scams.
“Royal Mail Group works hard to prevent and detect fraud,” a spokesperson said.
“Royal Mail will only send email and SMS notifications to customers where the sender has requested this when using our trackable products that offer this service.
“The only time we would ask customers to make a payment in an email or SMS is if a customs fee is due.
“In this case, we will also leave a grey card telling them there’s a fee to pay, either for the international customs fee or a surcharge for an underpaid item, before we can release the item.
“This may arrive later than the email or SMS.”
The company has a page on its website dedicated specifically to highlighting known scams using its name.