Two planes have narrowly avoided a collision on the tarmac of Australia’s busiest airport as it struggles with staff shortages.

The Jetstar and Qatar Airways planes almost collided at Sydney airport at 7am on Sunday.

A Jetstar spokesperson said its plane was following instructions from air traffic control when the pilots were forced to brake “firmly” when another aircraft came into “close proximity”. “We have commenced an investigation into the incident,” they said.

Initial inquiries suggested the tug vehicle pulling the Qatar aircraft may not have followed instructions, a source said.

The Australian Transport Safety Bureau (ATSB) said it was investigating the “near collision”.

“As reported to the ATSB, a Jetstar A320 was taxiing prior to a planned flight to Gold Coast airport when its flight crew observed a Qatar Airways Boeing 777, under tow from an aircraft tug, in close proximity on a crossing taxiway,” the safety bureau said.

“Both aircraft were stopped abruptly. A cabin crew member aboard the A320 was injured, and there was damage to the connection between the 777 nose gear and the aircraft tug.”

Investigators would interview flight crew, tug operators and air traffic controllers, plus other witnesses, and review any CCTV footage, the bureau said.

Airservices Australia said it was working to safely manage demand at the airport “following a reported safety incident between two aircraft moving on taxiways”.

“We are working with airlines to reduce delays and the impact on passenger travel as much as possible,” a spokesperson said on Sunday. “Airservices is reviewing the incident and will assist with any safety investigation.”

Jetstar flight JQ402 was taxiing on the tarmac when the near-miss occurred. The incident left one crew member needing medical attention at the scene, Jetstar said. No passengers were injured.

The flight was cancelled and passengers re-booked on later services.

The incident came after delays to more than 150 flights passing through Sydney on Saturday as the airport struggled with staffing shortages.

A spokesperson for the airport said Airservices Australia, which oversees air traffic control, was managing reduced air traffic movements. Flights across the network would be affected and delays were expected, the airport spokesperson said.

Airservices Australia had been unable to roster enough staff for three consecutive days, the Airlines for Australia and New Zealand chief executive, Stephen Beckett, told ABC News on Sunday.

The NSW premier, Chris Minns, said he was “obviously concerned” by Sunday’s near-miss.

“Not just the safety risks but we want to make sure the airport is operating at full capacity,” he told reporters.

“That’s hugely important for our economy. We don’t want to see people disrupted if they go to the airport and services are cancelled because there are not enough air traffic controllers.”

Minns said the government was “hopeful that there’s a plan in place to recruit more people for a highly specialised but very important job”.

“We’re opening a brand new [western Sydney] airport in the not too distant future, so there’ll be even more strain on that service than there is today. It’s hard to employ people, particularly for these specialised services, because we’ve got a very tight labour market, but this isn’t a nice-to-have; it’s a must-have. It’scrucial for public safety and our economy.”

Sydney airport faced significant delays on Friday with some passengers forced to sit on the tarmac for more than an hour as more than 120 flights were delayed.

Qatar Airways was contacted for comment on Sunday.