Speaking to the Herald, Norman said it would appear from the outside that Jones was having "quite a big influence on fisheries policies".
Jones said he had received donations from the company but they were in compliance with Parliament's rules on donations.
He said Norman was using "politically lurid language," which was "all part of their [Greenpeace's] process to fundraise".
"Greenpeace has a track record of misinformation and exaggeration.
"It's extraordinary that the Greenpeace's Australian spokesman Russel Norman is ranting in such a way to damage the good name of New Zealand."
Norman said this "obviously was not" his intention and said it was just a distraction from the fact an Amaltal fishing vessel was caught doing bottom trawls in a protected area of the Tasman Sea.
Amaltal is a subsidiary of fishing company Talley's.
Norman was born in Australia. He is also a former co-leader of the Green Party.
This is certainly not the first time Norman and Jones have been at odds.
In September 2017, when Jones was explaining whether he could work with the Greens, he said: "I had absolutely no time for Skippy [Russel Norman]."
Jones was pleased when Norman left Parliament: "I'm not going to have an Australian running the New Zealand Green Party, lecturing me about environment and economics in the north."
On the issue of fishing in the wrong area, Jones said this was a "mere technical issue which would be ironed out when common sense prevails".
In a statement, a spokeswoman for the Ministry for Primary Industries (MPI) said MPI had initiated a prosecution against Amaltal, as well as the person who was the master of the vessel at the time of the incident.
Both are facing charges under the Fisheries Act, the spokeswoman said.
In its own statement, Amaltal confirmed one of its fishing vessels had inadvertently fished in an unauthorised area of the Tasman Sea in May last year.
Amaltal said the vessel's captain had sought confirmation from an onboard MPI observer that the area remained open and the vessel was entitled to fish there.
Amaltal said the observer confirmed fishing was permitted in the area.
"The observer unit of MPI had provided the observer with incorrect information regarding the closed and open areas," Amaltal said, adding that it "categorically rejected any suggestion that there was deliberate and intentional fishing in any closed area".
MPI said the statements made by Talley's would be tested in court.