Farmers have blocked roads with tractors and grain shipments have been virtually paralysed during the protest.
Strike leaders say the protest will continue until the government drops new export taxes, which substantially raise levies on soya and sunflower products.
Anibal Fernandez, the Argentinian justice minister, told local radio that the government was willing to negotiate but it would not allow the farmers to say "how things should be done".
Alberto Rodriguez, director of the Cereal Exporters Center (CEC) and vegetable oil producers' group, CIARA, said: "At the moment, the majority [of grains exporters] are not operating. Because of this] we've ended up with no stock, no grains, no oils and no meal."
The conflict is the biggest crisis faced so far by Cristina Kirchner, the president who took office in December, and marks a deterioration in relations with farmers who have criticised measures such as export bans and price controls.
Consumer and retail groups say reports of bare shelves at supermarkets and grocery stores were increasing as the strike dragged on.
The strike also weakened the value of the peso currency due to fewer inflows of dollars from agricultural exports.
Farmers have carried out road blockades on a regular basis and, in some areas, frustrated truck drivers have begun clearing motorway barricades themselves.
The demonstrators have been letting trucks pass as long as they are not carrying farm goods.
Farmers at roadblocks have handed out pamphlets, saying the new export taxes "take [money] from rural communities, from our shop owners and our industries.
"With this money there could be more investment, more jobs and a better future for everyone," the pamphlets add.