Mr Coffey said he and Mr Cunliffe were "on the same page" in regard to oil exploration in the sanctuary - requiring the industry to have to prove it would cause no harm to the Maui's dolphin before any new consents would be granted.
"How is anyone going to prove it is safe? That's a rule that will ensure that we will work towards protecting the critically endangered Maui's dolphin," he said.
"Put the onus back on the petroleum companies to prove there's no harm to Maui's dolphins, like the new regulations around legal highs."
Mr Bridges said Mr Coffey was "trying to dig himself out of the hole he's got himself into".
"On the weekend, he was calling for me to be sacked and for an absolute ban on drilling.
"Now it's clear David Cunliffe supports continued petroleum activity, will Tamati Coffey be seeking a resignation from his leader?
"Or does he accept that he's had a complete about-face in his position?
"I wonder what his position will be tomorrow?"
Mr Bridges said Mr Coffey's stance was still different to that of Mr Cunliffe.
"David Cunliffe has accepted there is no proof of harm for petroleum activity so it should continue."
A man involved in Saturday's protest, who did not want his name used, said he was "lost for words" about Mr Cunliffe's stance.
"I just don't get it. But one thing I do know is that our politicians of New Zealand need an overhaul.
"We need a fresh change in this country."
Dr Grant Duncan, an associate professor in the politics programme at Massey University, said within Labour there were differing values in terms of economic growth and the "extractive industries" - fishing and oil exploration.
"There's growth on one hand and conservation of endangered species on the other.
A spokesman for Conservation Minister Nick Smith said there had not been a single sighting of the Maui's dolphin in the Block Offer area, based on 809 official observer trips.
"There is a historic record of Maui's dolphin sightings - 975 since 1970.
"The minister has been advised that about a dozen of these could be in the Block Offer area.
"However, the exact location of these cannot be verified."
Mr Cunliffe could not be contacted for comment.