Milk could temporarily cost an extra 10 cents a litre to help drought-hit dairy farmers, after an online petition jolted the federal government into action.

More than 25,000 people have signed a week-old petition set up by the Queensland Dairyfarmers’ Organisation, which calls on Australians to shell out the levy which would go directly to farmers in drought.

Prime Minister Scott Morrison doesn’t want to push up costs for households, but says Agriculture Minister David Littleproud will take the proposal to cabinet.

“I don’t want to see people paying any more for milk and I don’t want to see dairy farmers getting ripped off,” Mr Morrison told reporters in Brisbane on Wednesday.

“They’re the objectives, so let’s go and get them done.”

The prime minister says his “first instinct is never to try and solve a problem with a tax”, but he wants to ensure the sustainability and viability of the dairy sector.

“But not … at a cost to mums and dads pouring milk on their Corn Flakes.”

The petition calls on Coles and Woolworths to collect the levy by increasing prices, and for milk processors to guarantee to pass the full amount back to farmers.

The department of agriculture is investigating how a temporary levy could be implemented.

Mr Littleproud has spoken with Coles and Woolworths, with Woolworths showing “leadership” on the issue while Coles “is more reluctant”.

He also plans to contact ALDI and Metcash, which runs IGA.

Woolworths will be on board with the proposal as long as other retailers are too, he adds.

Opposition Leader Bill Shorten says Labor is open to the idea of the levy, using it as an opportunity to have a dig at the government over its grant to the Great Barrier Reef Foundation.

“Drought relief is a more useful proposition to me than giving a charity in a half-hour meeting half-a-billion dollars,” he told reporters in Townsville.

Nationals leader Michael McCormack is open to any ideas to help farmers struggling with the drought.

“I support anything that’s going to get more profitability at the farm gate,” he told Sky News.

Deputy NSW Premier John Barilaro backed the measure, saying supermarkets should end the price war with farmers to help build long-term resilience in the industry.

“The best thing we can do for the farm sector and primary producers is to pay them the price it costs to actually deliver that produce to the shelves and to the table,” he told reporters in Sydney.