Fisheries Minister Jonathan Shaw has agreed that dumping thousands of tonnes of dead fish back into the sea because of EU fishing quotas is "immoral".
He said he supported the view of EU Fisheries Commissioner Joe Borg and would be pushing for quota increases.
The fishing industry has warned it faces ruin because fish caught after quotas are exceeded have to be dumped.
But environmentalists say quotas are necessary to protect stocks, and want to see a change in fishing practices.
European Union quotas strictly limit the amount of fish that vessels can bring back to port, but there is no restriction on the amount of fish they actually catch.
BBC rural affairs correspondent Jeremy Cooke found that boats fishing in the "mixed fishery" of the North Sea often accidentally catch a species or size of fish which is above their quota and have to throw the "discard" back.
The EU estimates that between 40% and 60% of fish caught by trawlers in this area is dumped back into the sea.
Mr Borg - who is instrumental in setting the laws and limits - described such discarding of fish as "immoral" but said there was no clear solution.
"The problem is when we come to work out the details of how to eliminate discarding but at the same time have sustainable fisheries - that is the big problem."
Mr Shaw said it was an "absolute waste" to throw good quality fish back into the sea.
He told BBC Radio 4's Today programme he would be pushing for an EU cod quota increase as well as looking at technological solutions, such as nets that would catch only certain kinds of fish.
"We have seen a recovery in cod in the North Sea in particular - now that is good news," he said.
"So that is why we will be pressing the commission at the annual round in December for an increase in cod and hopefully that will help the fishermen."
Scotland's fisheries minister Richard Lochhead agreed that that an increase in the fish quotas was "essential, and justified by the science."
And he claimed his government was "leading the way" on fish conservation with a range of ideas developed with fishermen and environmental groups. These included voluntary closures of fishing areas and independent on-board observers to make sure young fish were not caught and then discarded.
Trawler skipper Phil Walsh told BBC News he had landed all of the cod he was allowed by June this year.
Since then, he has been fishing for prawns and dumping prime whiting, haddock and cod, which would fetch as much as £13.50/kg on a supermarket shelf.
"I can't describe the feeling really," he said.
"It's your livelihood and you spend your life trying to catch it and then you have to throw it back over the side.
"It's an impossible situation and, unless it is sorted out soon, we will all be finished."
Many Scottish and English fishermen say they have seen a huge increase in the number of cod in the North Sea this year and now want an increase in the quota level for cod and other white fish they catch.
EU FISH QUOTAS
The European Commission's Fisheries Council meets to discuss fishing quotas every December
In 2006, it cut the amount of cod that could be caught in 2007 by between 14% and 20%
This meant UK fishing crews could catch 7,773 tonnes, down from 9,037 tonnes
The number of days cod fishing boats could spend at sea was also reduced by between 7% and 10%
This meant crews with the biggest nets could spend 155-156 days at sea, down from 163 days
However, many environmentalists want to see a total ban on cod fishing
"I feel very bitter because we've been so long trying to protect the cod," said trawler skipper David Mell.
"[We've had] decommissioning, increased our mesh size, we've been through a lot of pain really.... [But] I thought I would never see the day that I had to throw adult cod overboard."
But environmentalists, who have for years been sounding the alarm bell over the decline of North Sea fish stocks, say now is not the time to increase the amount being caught.
They say quotas are essential to ensure spawning stocks are allowed to mature and to breed.
But, like the fishermen, activists such as the World Wildlife Fund's Helen McLachlan agree that throwing dead cod back into the water is not the answer.
Instead, she said, there must be a change in fishing practices.
"Nobody wants discards," she said.
"So let's not catch the fish in the first place.
"Let's avoid areas where there are going to be large spawning stocks of fish, let's avoid juveniles... let's use selective gear so [a fisherman can say], 'I will only catch prawns, I will not catch white fish'."
Oliver Knowles, a campaigner for Greenpeace, also believes quotas are not working for the UK's mixed fisheries.
He says the only answer is to stop fishing altogether in 40% of the world's oceans.
"Most importantly, I think you have got to create marine reserves. We don't have any proper protection for the marine environment.
"We are talking about a very large scale - about 40% - and Greenpeace isn't alone in calling for protected areas at around that size."