Speaking at a rally in the capital, Kirchner said that Argentina would no longer tolerate the strike, which has entered its 20th day.
"Don't do more harm to the people, lift the roadblocks so Argentinians can get food," she told the crowd of union members and local rights activists.
Farmers have vowed to continue the protests, which have caused food shortages, paralysed food exports and plunged the government into crisis.
It has become the most serious political challenge so far faced by Kirchner, who took office in December after succeeding her husband, Nestor Kirchner.
Clashes
The standoff began after a March 11 presidential decree that dramatically increased export taxes on soya beans from 35 per cent to as much as 45 per cent, and also placed new duties on other farm exports.
The crisis deepened after clashes between middle-class Argentinians who came out in support of the farmers - many of whom are wealthy landowners - and Kirchner's supporters.
The country has also been hit by food shortages after farmers blockaded the main routes in and out of cities, with dairy and meat produce scarce and supermarket supplies dwindling rapidly.
Argentina is one of the world's main exporters of soya bean products and a leading supplier of corn, beef and wheat.
The Argentinian government says that the higher taxes on soya exports will help control inflation on domestic food goods and redistribute wealth in the country.
It offered concessions on Monday to smaller farmers in the form of rebates for the higher taxes and compensation for travel costs, but the offer was rejected by protest leaders.