There are now nearly 230,000 people on bridging visas in Australia, and there are fears many of these people are being exploited in workplaces.
"Peter Dutton has lost control of borders at our airports," Senator Keneally told Sky News on Sunday.
"We've got to give Scott Morrison and Kevin Rudd credit for stopping the boats.
"But Peter Dutton seems to have missed the fact the people smuggling operation has shifted from boats to planes under his watch."
A spike in the number of asylum seekers arriving into Australia by air will be targeted by a Labor roundtable meeting with migration and border security experts on Monday.
"Ninety per cent of these people are found not to be refugees," Senator Keneally said.
"But they are coming largely from Malaysia and China - they are being sent here by criminal syndicates and illegal labour hire companies."
Senator Keneally said people were being sent off to work in "quite exploitative, sometimes slavery-like conditions" in horticulture, hospitality and sexual servitude.
Of the nearly 230,000 people on bridging visas, some are asylum seekers, others are applying for skilled visa positions having been here as students or temporary workers, and some are waiting for partner visas.
Labor argues the Department of Home Affairs needs more resources to deal with asylum claims.
For its part, the government wants to pass legislation that would stop anyone who arrived by boat since 2013 being given permanent residency in Australia.
"Labor made an offer to support this legislation, if the government took up the New Zealand offer to find a durable solution for these people (who remain in Papua New Guinea and Nauru)," Senator Keneally said.
"The government refused to do that, and now they have the problem of 1000 people who are here (for medical treatment) that they have to solve."