Speaking to ABC on Saturday morning, Shadow Minister for the Digital Economy Ed Husic compared the laws to the disaster of introducing the cane toad to Australia.
"A number of us were very concerned about the way in which the government was dealing with a sensitive issue, an economic security issue of encryption," Husic said.
"A lot of countries have tried to grapple with this issue ... they have not wanted to do what the Australian government has wanted to do, which is to inject a cyber cane toad into sensitive encryption environments. And we've been saying you've got to walk carefully on this and they've refused to."
Husic said his party had a "terrible choice", but did the "best possible thing" for the country by letting the laws pass in the belief they will be amended in February.
"We'll be watching very carefully as to whether or not the government's using this period as a sort of lab environment to test out what it can do on encryption," he said.
"[We are] concerned also that some of these apps may be blocked out from Australian users because the firms themselves are concerned about potential reckless engagement by the government on this issue."
On Thursday, Husic had detailed the problems of oversight and how examination is required by informed individuals, comments he echoed again on Saturday.
"The type of judicial oversight offered in this process is tissue-tough. I don't think it cuts the grade of what people would expect," Husic said on Thursday.
"People want a specialist judge backed by a team of people who can assess warrants and applications made to gain access under the TCN arrangement. They want to know that people who are capable of making judgments on applications can do so."
Husic also repeated calls for there to be reporting on how many notices and requests are issued.
Speaking elsewhere on Saturday, Shadow Finance Minister Jim Chalmers accused Prime Minister Scott Morrison of doing a runner when the government adjourned the House of Representatives to avoid a Bill from the Senate on the release of refugee children in detention on Nauru from being sent back to it.
"Scott Morrison may have been prepared to jeopardise Australia's security by doing the runner from Parliament and escaping Parliamentary scrutiny, but Labor was not," Chalmers said.
"It was a difficult decision for Labor to take, but we did the right thing as we always do, and we've given ourselves the capacity to improve the laws at a later date by having our amendments considered and by ensuring that the good work of that Parliamentary committee -- quite often, the good bipartisan work of that Parliamentary committee -- can continue in the coming months."
Labor dropped its amendments on Thursday night in an understanding that the Bill would be amended in the new year; however, Attorney-General Christian Porter said after the legislation was passed that the government would only consider the amendments.
On Friday morning, Opposition Leader Bill Shorten conceded that the laws were rushed.
"It is not a perfect solution. And to all of those who are concerned about the economic impact of this legislation, we hear you -- and we've said we want to review it," Shorten said.
"But in the meantime, I think Australians are over the games and people standing in two different corners yelling at each other and throwing rocks and insults.
"I will take half a win, and move forward, than simply continue this sort of angry shouting."
Over the weekend, ProtonMail hit out at the encryption laws in a blog post.
"[The Assistance and Access Bill] is one of the most significant attacks on digital security and privacy since the NSA's PRISM program," the company wrote.
"We thoroughly condemn the new law, and as the world's largest encrypted email provider, we remain committed to protecting our users anywhere in the world, including in Australia."
The company said that even though the laws are restricted to Australia, it will have wider impacts.
"Australian Parliament has single-handedly undermined global confidence in any software maker with an Australian presence, including Facebook (by extension WhatsApp and Instagram), Google, and Apple," it said.
ProtonMail said since it based in Switzerland, any request from Australia would need to comply with Swiss criminal and data protection laws.