The federal Minister for Tourism Simon Birmingham has told NSW authorities to lift their standards after an error led to two international travellers accidentally bypassing quarantine requirements after landing in Sydney.

On Saturday, a 53-year-old woman and her 15-year-old son from Germany were initially directed to board a bus to hotel quarantine after being screened by NSW Health.

Authorities said a miscommunication led to police instead escorting the pair to a Melbourne-bound domestic flight.

It is understood a security guard at a Melbourne Airport car park overheard a conversation involving the pair and was able to escalate it up the chain of command.

• NSW ‘left the front door open’ in quarantine bungle

The pair have tested negative to COVID-19 and are in hotel quarantine in Melbourne.

International travellers are still banned from flying into Australia but the German-born mother and son were allowed into the country because they are both Australian citizens.

On Sunday, NSW Police said it was “very sorry for the incident”.

Senator Birmingham said the “apology is welcome” but the incident was evidence of gaps within the NSW’s quarantine procedures.

“What is more important is… to make sure that there’s not a repeat in that regard,” he told the ABC.

“These are reminders that the processes needed to be thorough, they need to be rigorous and the safeguards need to firmly be in place.

“Obviously, further tightening is required in NSW.”

Simon Birmingham said ‘further tightening’ was needed in the NSW system. Photo: AAP

He said there was “no cheap and easy way to have Australians coming in in massive volumes” and rebuked Labor’s calls to raise the cap for citizens returning from overseas.

On Sunday, NSW Police admitted it “incorrectly” allowed the pair to board the flight and attributed the the error to a “language barrier”.

Deputy Commissioner Jeff Loy said an officer mistakenly thought they were exempt from quarantine.

He said the officer was only on his second shift at the airport operation and “thought he was doing the right thing”.

“There was a language barrier,” he said.

“There was communication issues and the police officer has admitted the mistake that he didn’t check the appropriate exemption forms and the paperwork appropriately.”

Deputy Commissioner Loy admitted the error was “not a good look” for NSW Police, but said only two passengers out of 100,000 had slipped through quarantine cracks.

The breach has overshadowed the reopening of runways at Melbourne’s Tullamarine airport on Monday. It has been closed to international flights outside of New Zealand for six months.

Chief executive Lyell Strambi said the incident was a “really good measure of the level of diligence in Victoria”.

“Any error of this sort of nature is disappointing, without a shadow of a doubt,” he said.

“I was actually quite impressed NSW Police took quick accountability for it, that means you get fast learnings out of it.”

A review of police practices at Sydney International Airport is underway as a result of the breach, NSW Police said in a statement.

Senator Birmingham said Australian Border Force officials would be working with all the state and territories.

-ABC