The crisis has also severely tested the government of Cristina Kirchner, the Argentine president.
Kirchner has staunchly defended the law, saying it will spread the benefits from high global commodities prices.
Alberto Fernandez, Argentina's cabinet chief, announced the modifications in a news conference, but also defended the tax, saying too much of Argentina's farmland had been given over to soy at the expense of other crops.
"I'm confident this resolves the concerns of a lot of farmers," Alberto Fernandez was quoted by Reuters as saying.
However Alfredo de Angeli, an Argentine farm protest leader, criticised the announcements as "still a disaster".
"It's all a tactic of confusing people," he told local television.
"Unfortunately, the agricultural sector continues without a solution."
Al Jazeera's Latin American editor, Lucia Newman, says most farmers view the concession as too little too late, although some said they would continue to analyse the government statement overnight and come back with a response.