Alliance councillor Tom Campbell made his remarks during a Policy and Governance Committee meeting in which he also called the DUP's Robert Hill "an idiot". And, despite calls for him to say sorry, he said he would be "offering no apology".
Earlier this month, the DUP filled ten of twelve council committee posts for which members receive extra financial allowances. The largest party on the council, they have openly admitted they have now brokered a two-year pact with the Ulster Unionist Party - with one of its members, Alderman John Scott, now serving as Mayor.
Mr Campbell said that following his comments concerning DUP "tactics" and councillor Hill, he left the meeting declaring an interest in an item on the agenda. After his departure, the DUP's leader on the council, Paul Girvan, proposed "that a letter be sent to him (Mr Campbell), asking for an apology."
Mr Hill, the politician who was branded an "idiot" said the outburst was "all a bit childish".
"Councillor Campbell indicated that things in the chamber were almost fascist," he said. "I asked him who he was calling a fascist and after that he called me an idiot. I said nothing after that because I wasn't going to get dragged into it."
Councillor Hill added: "It's childish behaviour - it's the type of thing you would expect to hear in the playground and not in the council chamber."
But councillor Campbell countered:
"I said that I suggested councillor Hill listened more carefully to my comments."
"The DUP's pettiness was evident at the AGM and is clearly being pursued by this attempt to prevent me from criticising them. But, it is an attempt which will fail. I will continue to criticise the DUP for what they have done."
He added: "I had to leave the meeting early because I declared an interest in an item on the agenda and I had other matters to attend to.
From my perspective, it is disappointing that a matter was discussed in my absence.
"During the debate there were angry words used and perhaps they could have been chosen differently but I will not be giving an apology to the individual (Cllr. Hill). What I said was that the DUP's tactics were akin to fascist tactics."
Councillor Campbell also revealed that he has been in contact with the Equality Commission over the DUP's dominance at Newtownabbey council, adding he could not rule out the possibility of legal action. He has also accused the party grouping of being in breach of the council's Good Relations policy.
Alderman Girvan said councillor Campbell was "asked to withdraw the comments", but refused to do so.
"I did say that I felt councillor Campbell was out of order and I proposed that a letter be sent to him asking for an apology," said Mr Girvan.
"It is inappropriate because if you don't treat members with respect it is insulting. You don't need to revert to petty name-calling. To go down to that level creates a problem with members working together."
Added Mr Girvan: "The DUP agreed a deal with the Alliance party between 2005 and 2009 and we honoured that deal. A deal is now in place with the Ulster Unionists and that is what we will work on until 2011."