UberX drivers have been allowed to pick up passengers from the terminal in a designated zone since Thursday, angering taxi operators.
Cab drivers stopped collecting passengers from Thursday night and continued their action on Friday, blockading the ride-sharing pick-up zone.
In response, Uber suspended its own services to ensure the "safety of riders and drivers".
"We'll continue liaising with airport security and the Australian Federal Police as they handle the situation and will resume public pick-ups as soon as possible," company spokesman Mike Scott said.
Taxi drivers appear to be arguing among themselves over whether to continue the strike this morning @SBSNews pic.twitter.com/wdLlb4NJBd — Rhiannon Elston SBS (@rhiannonelston) August 10, 2017
The protest was called off early Friday afternoon, but Uber said it would not resume its own operations until next week after consulting with airport security officials.
"We'll continue working with the airport and trust they'll be able to provide a safe and secure pick-up experience for riders and drivers when we resume," an Uber spokesperson said.
At the height of the taxi protest, airport authorities threatened to call on the Federal Police to end the blockade.
"This is a really bad look for Adelaide," airport spokesman Brenton Cox said.
"If the travelling public are materially impeded and continue to be then that's definitely something we will be looking into with the authorities."
The Taxi Council of South Australia says the move to allow Uber at the airport is disappointing and there are concerns about the accreditation of drivers.
"It's our understanding that only a handful of UberX drivers have sought and secured their accreditation to operate in the ride sourcing market," council president Jim Triantafyllou said.
UberX had only been allowed to pick up passengers from Thursday, however Uber's more expensive black service was already available from the airport.
Adelaide airport joins Sydney, Perth, Canberra and Perth airports in allowing the ride sharing app.
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It comes as Victoria announced it will impose a $1 levy on all commercial vehicle trips after legalising ride-sharing service Uber.
The levy will come into effect next year, replacing licence fees and helping compensate taxi operators.
Public Transport Minister Jacinta Allan says the reforms create a level playing field for taxis to compete with ride-sharing services and will encourage new operators to enter the market.
The bill was passed on Thursday after the government accepted upper house amendments including the halving of a proposed $2 levy.
Under the reforms, ride-share drivers will be required and be accredited, while the government will buy back licences from taxi drivers wanting to exit the industry.
Drivers will receive for $100,000 for a first licence and $50,000 each for up to three additional licences.
The government also agreed to remove a $50 million cap for their fairness fund to ensure all eligible applications receive payments.
Liberal deputy leader David Hodgett said the government's levy would hurt vulnerable people who relied on taxis and ride-sharing services.
Uber in a statement said it was pleased to see the "important reforms" passed "for the benefit of the travelling public, drivers and the industry as a whole".
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