Labour TD Kathleen Lynch confirmed she is seeking legal advice on whether the manager can be compelled to collect the waste.
"Under the Waste Management Act, the city manager has a duty to keep all public areas free of litter. This is a legal obligation that is not being complied with," she said.
The Green Party called on the Environmental Protection Agency (EPA) and the Health Service Executive Southern Region to intervene.
But the council stood by its policy of non-collection.
"Our policy is quite clear. We will not collect untagged rubbish," a spokesman for the environment department said.
Uncollected rubbish has piled up on a number of city streets since the introduction of the council's bin tag policy on January 17.
The non-collection has sparked a wave of illegal dumping. Inner city areas like Shandon Street, where a E15 million revamp is almost complete, parts of Blackpool, Evergreen Street, Douglas Street, St Luke's, and the city's flat and apartment areas are worst affected.
But the council moved yesterday to track down those responsible.
Dozens of rubbish bags that had been left on Shandon Street were among the first to be collected.
Council environment staff were still sifting through the rubbish last night in a "secure and quarantined area" looking for evidence for possible court proceedings.
"The standard procedure here is to issue an on-the-spot fine first (E125). If that isn't paid, then we will issue court proceedings where the maximum fine is E3,000," the spokesman said.
But he admitted the council faces a tough task to secure prosecutions.
"The evidence we're getting is lower than what we got before," he said.
About 490 on-the-spot litter fines were issued last year. No court proceedings followed.
The council employs four litter wardens one post is vacant, one has been transferred to another different department, leaving just two on active duty yesterday.
Green councillor Chris O'Leary said the uncollected waste is creating a health and safety crisis.
"Leaving the waste on the streets is simply not an option," he said.