Aontú has pledged to campaign for more funding for councils but wants a probe into how so many local authorities became burdened by debt.
Launching its local government election manifesto in Belfast on Tuesday, Aontú leader Peadar Tóibín said his party had written to each of its rivals inviting them to debate ahead of next week's poll but that so far only Naomi Long has responded, signalling that she'd be happy to take part.
The all-Ireland anti-abortion, republican party is running 19 candidates on May 18 and is defending two seats.
It advocates the devolution of economic power from London to Belfast, ultimately seeking "self determination for all-Ireland".
Aontú's pledges for local government include a freeze on rates increases during the cost of living crisis, working with the Department of Communities and housing associations to increase the number of new homes, and using councils to oppose health and education cutbacks.
Local authorities will also play a role in furthering Irish unity, promoting Irish language rights and blocking the British government's controversial legacy legislation, Aontú said.
Speaking on Tuesday, Mr Tóibín said the north was in the middle of a "major political and economic crisis".
He said the DUP's boycott of the Stormont institutions meant "citizens are being denied democracy".
"One-in-seven people are on hospital waiting lists; 300,000 people are living in poverty, 45,000 people are on housing waiting lists and key public servants are forced to strike for decent pay," the Meath Wst TD said.
"In any other western country this level of hardship and political dysfunction would be met with protests on the streets but this is not any other western country."
Describing the north as the "only western state where one political party can crash the political institutions, refuse to work and still keep taking their wages", Mr Tóibín restated his party's call for MLAs' wages to be stopped while Stormont is suspended.
