Agriculture Minister Stéphane Le Foll declared that he had "perfectly understood" the protesters' message and would propose changes to the law, while Finance Minister Pierre Moscovici said that "adaptations" had been made.
The government is expected to reduce the tax by at leat 50 per cent for Brittany, which is a long way from Paris and the south of France, but Moscovici insisted that he would not scrap it or put off its proposed introduction on 1 January.
Farmers' unions on Monday called for its introduction to be postponed for two years because of the jobs crisis in the farming and food-processing industry, which has been expecially intense in Brittany.
Protesters on Sunday vowed to demonstrate in the Breton town of Quimper next Saturday, following this weekend's violent protests, in which protesters clashed with police.
Under the new plan heavy goods vehicles weighing over 3.5 tonnes will have to pay a fee for transporting goods around France.
"I think that the minister hasn't understood what’s at stake," Thierry Merret of farmers' union FDSEA told RFI on Sunday. "He’ll have to change his mind. It’s obvious that for us in Brittany his answer is an insult."
Merret accused Le Foll of "a complete misunderstanding of the dossier".
"Today they want to tax agriculture… actually, the entire Breton economy," he added.
Under orders from Europe to reduce its budget deficit, the French government has cut spending and introduced a number of new taxes, arousing opposition from savers, football clubs and right-wing politicians.