But the Community and Public Sector Union (CPSU) is threatening more strike action next month if pay negotiations don't resume.
"We are sorry if there has been any disruption this morning," a union spokesman told AAP.
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"It's certainly not our intention to inconvenience the public but this is really a last resort for us."
Passengers at international terminals faced delays of up to two hours on Tuesday after about 3000 workers took industrial action at Sydney, Melbourne, Brisbane, Perth, Adelaide and Cairns.
Travellers arriving at Sydney Airport on Tuesday reported chaotic and emotional scenes as frustrated passengers tried to get through customs.
"It was chaos in there," said Sydneysider Simon Lister, who flew in from Los Angeles.
"A lot of people who were queuing were getting irate and staff were getting irate too, they were getting very angry and pushing a lot of people out of the way."
Yacov Barber flew in from New York and missed his connecting flight home to Melbourne.
"Everyone was just pushing and shoving," he said. "It became quite emotional for many people."
Outside the airport, up to 200 customs workers gathered in protest, chanting and waving flags.
"What do we want? Fair pay. What do we really want? Respect," the group yelled.
The action follows a stalemate in negotiations on a new enterprise agreement with Australian Customs and Border Protection after the previous agreement expired in June.
CPSU members have rejected a government offer of a nine per cent pay rise over three years, saying it does not keep up with the cost
of living.
"They're very upbeat, they're very determined to get a fair outcome," a union spokesman told AAP.
"They're upset that they have to take industrial action. They prefer to negotiate a settlement."
Two hour-long stoppages took place in Sydney at 6am (AEST) and 8am on Tuesday.
Further delays are expected when another hour-long stoppage takes place on Tuesday between 7-8pm (AEST).
"What we're hoping will happen after today is that management in customs get the message that we're absolutely serious about getting a fair outcome," the union spokesman said.
"That they will pick up the phone, give us a call and start negotiations again and we can get this resolved...
"We've had some supportive comments from passengers coming through the airport today, which is great."
The union has threatened further industrial action from Oct 5-8 if negotiations don't resume.
This would affect all customs operations nationally, including airport operations, ports, district offices and the container
examination facilities, the union has said.
Sydney's international airport is expected to be affected by further customs strikes on Thursday and Saturday, as is Cairns airport.
