The law allows an indigenous community to approve the sale of tribal lands by simple majority vote - eliminating a provision that had made it nearly impossible to develop communal property.
Garcia said on Wednesday that a repeal would condemn Peru's Indian and rural communities to "another century of backwardness and misery".
Protesters are threatening to stop the flow of natural gas and oil through two pipelines in the Amazon jungle. Their action threatens energy supplies.
Thousands had clashed on Wednesday with police in the jungle city of Bagua and nine civilians were treated for injuries.
Peru's congress has agreed to vote on the law's possible repeal - on the condition that protesters unblock roads and suspend demonstrations.
State of emergency
Garcia decreed the law using special legislative powers he was granted to implement US requirements for a free trade pact between the two nations.
A state of emergency had been imposed when protesters occupied oil and electricity plants in the Amazon basin.
Alberto Pizango, leader of the Inter-Ethnic Association of the Peruvian Forest, said: "We're not afraid of the state of emergency."
After talks with Javier Velazquez, the congress president, in Lima on Wednesday, Pizango agreed a 48-hour truce.
About 12,000 indigenous people have been protesting since August 9. Their land is estimated to contain billions of dollars' worth of timber, minerals and oil.
On Sunday, clashes between 800 demonstrators and police left at least four people injured.
The state of emergency, which lasts for 30 days, covers the eastern provinces of Bagua, Utcubamba and Datem del Maranon and the southern district of Echarate.