Telstra has resumed delivering SMS messages to customers after a fire caused nationwide service outages and triggered some texts to be sent to random numbers.

A number of customers reported receiving random texts after a "serious" fire at an exchange in Chatswood around midday.

"There was a serious fire and that impacted the exchange," Telstra CEO Andy Penn said.

"This is one of the major exchanges in the country, there is a lot of traffic that flows through there."

During the outage, customers said they were not able to make or receive calls, use data services or send text messages.

Mr Penn said 30 percent of Telstra customers were affected by the outage.

The outage also caused delays at airports across the country after Jetstar reported issues with their check-in software.

Just after 3pm, Telstra said services were "beginning to restore" but they were still experiencing issues with SMS messaging.

"In the context of the damage, it appears some SMS messages were corrupted, which resulted in potentially some of those going to the incorrect address," Mr Penn said.

"It's extraordinarily unusual, I've never known that to happen before."

Some customers took to Twitter to share the messages they said they incorrectly received from random numbers.

Telstra said it will be 'holding' all SMS messages until the issued is resolved.

The outage also temporarily affected check-in services with Jetstar at major airports across the country.

The airline reported on Twitter that nine Australian flights had been delayed by 45 minutes.