A Telstra spokesman said it's important to note the Telstra SMS platform is working and customers can still use this in order to send messages.
"Some customers may be experiencing an issue with Apple iMessage and FaceTime. Customers continue to have the option to send SMS messages," he told news.com.au.
"We're working to resolve the issue as quickly as possible, and apologise for any inconvenience. We'll provide more information as soon as it's available."
Telstra has since said the issue has been resolved.
"Earlier today some customers experienced a disruption to Apple iMessage and FaceTime services. We worked with Apple to resolve this issue. Services are now being progressively being restored. We apologise for any inconvenience this caused," he said.
Telstra says many of its customers can't send iMessages this morning.
Aussieoutages.com has recorded a spike in Australian residents reporting problems with the Apple app.
The telco says people should still be able to use standard SMS texts.
Hi Natasha, we are currently investigating an issue with sending some iMessages. We unfortunately don't have an ETA at this stage however our team are working on the matter as we speak. I apologise for the inconvenience and thank you for your patience. - Tony— Telstra (@Telstra) February 20, 2018
The glitch is being reported by users across the country as well as overseas.
Some users say Apple's FaceTime app is also being affected by the outage.
If you press and hold on the message that is stuck sending, you can choose to send it as a text message immediately. If you hit "more" you can highlight the message and delete it too.— Telstra (@Telstra) February 21, 2018