Since the start of July, about 80 people every day have claimed protection after landing at an Australian airport.
The trend appears likely to push annual arrivals to a record high.
Labor’s home affairs spokeswoman Kristina Keneally claimed people smugglers were “running riot” trafficking vulnerable people on the government’s watch.
“There’s nothing wrong with claiming asylum – it’s an important right,” Keneally said on Tuesday.
“However, in 90 per cent of these particular cases, the individuals are not legitimate refugees and are often being trafficked to Australia for the explicit purpose of being exploited.”
The number of asylum seekers who arrived by air climbed from 8562 in 2015 to 27,884 in 2018.
It fell to 24,520 in the year to June 2019, according to figures provided to Labor from the Department of Home Affairs.
The rate of applications since July suggests there will be more than 29,000 claims for asylum this financial year, unless the arrivals slow.
“This is a crisis that Peter Dutton is responsible for and it’s past time for the government to take action,” Keneally said.
“Mr Dutton is obsessed with blaming Labor, but he cannot run from his failures to control Australia’s borders, which is leading to widespread exploitation, slavery and even sexual servitude across the country.”
Immigration Minister David Coleman said it was a bit rich for Labor to lecture others on border security.
“We won’t be taking any advice from Labor, whose mismanagement of our border was an absolute disgrace,” he said.
“Despite having brought havoc to our refugee system, Labor continues to stand by policies that weaken our border protection.”
Coleman said less than 0.25 per cent of people who arrive lawfully in Australia apply for protection, and the vast majority are refused.
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