Pig producers have accused George Eustice of playing down the ongoing cull of pigs on farms caused by insufficient processing capacity in pork plants.
In an in-depth interview with the Politics Home website, the Defra Secretary said he expected to have "got the situation back into balance" by early spring.
Mr Eustice insisted government ministers "were always clear" there was never going to be a quick fix.
“In the context of the total number of pigs that are being slaughtered, which is in the millions, it’s a relatively small number [being culled],” he said.
Responding, the National Pig Association (NPA) said Mr Eustice was 'playing down' the crisis, as over 30,000 pigs had been culled due to overcrowding on farms.
The trade body added that this figure was likely to be a significant under-estimate as these were just the reported cases.
The Politics Home article cites NPA warnings about how the financial hit to pig farmers had forced some to walk away from the industry.
It refers to "harrowing reports from affected farms have revealed the stress and misery of their plight."
However, Mr Eustice did express sympathy for farmers who have had to cull pigs: “Culling on farm is never ideal, and obviously it’s distressing," he said.
"Farmers raise their pigs to go into food production, so to have that waste is something nobody wants to see."
The NPA said it would continue to push Mr Eustice to ensure the package of support measures announced in October 2021 would help the industry as intended.
The situation remains critical despite the support package, which included measures such as 800 new butchers' visas, a private storage aid scheme and incentives for processors to put on extra kills.
The measures were all designed to increase throughput in processing plants and, in turn, help reduce the severe backlog of pigs on farms.
However, the NPA said the support measures announced have had 'little impact so far'.
The sector's current crisis is a result of slaughterhouse and butchery worker shortages linked to Brexit and the impact of the pandemic.
Feed prices are also continuing to increase while pig prices plummet, adding to the already dire financial situation facing many farmers.
It follows the NPA's New Year message, which saw the body's chairman Rob Mutimer set out the sector's hopes for this year after the 'turmoil' of 2021.
"Covid-19 was initially quite friendly to the industry, but the bite in the tail of the loss of Chinese exports and illness and staff shortages reducing the throughput of the processing sector has really hurt us.
"With this being further compounded by Brexit, increased production costs and drop in the pig price, the industry has had a great deal to cope with over the past 12 months.
"A serious backlog of pigs remains on farms, which is still causing huge problems for some farmers who have run out of options, and the financial situation is dire."