News.com.au reports that Greens alderman Greg Jarvis' proposal would mirror pre-meeting prayer rosters at Palmerston and Alice Springs councils.
Palmerston has been addressed by a Rabbi, an Imam, a Buddhist monk, most Christian denominations and the Salvation Army Band.
"I just think it's really important that we acknowledge the multicultural nature of Darwin," Alderman Jarvis said. He called for a recognition of indigenous traditional owners before meetings.
"One option is a rotating (prayer) story; another option is to just acknowledge country and get rid of the Lord's Prayer," he said.
Alderman Jarvis also said it was time to move the picture of the Queen to a less prominent position in the council chamber, drop the Mayor's Right Worshipful title, and doing away with the council's Latin motto "Progrediamur" (Let us go forward).
Alderman John Bailey ridiculed the plan, saying democratic government and religion should be kept separate.
"It's probably more correct to do a recognition of country than to do the Lord's Prayer," he said.
"What about the prayer for the Flying Spaghetti Monster? We'd better include the prayer for that as well."
Ron Mitchell organises the Palmerston prayer roster.
"I think it's a way for the council to show that they recognise diversity," he said.
"Usually it's a prayer that relates to community harmony and peace and finding common ground."
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