Indian groups have in recent weeks voiced opposition to a government plan to allow foreign mining and energy companies to operate in Peru's Amazon region.
The protesters, who say that the firms will destroy their land in the rainforest, have claimed that several activists are missing in the wake of the clashes.
Peru's congress last week overturned two land laws that sparked the demonstrations.
Garcia has struggled to win widespread support among the electorate for his performance since he came to power in 2006.
His approval rating dropped to 19 per cent in November, amid complaints from Peruvians over his economic record and rising inflation.
The latest poll, published in El Comerico newspaper, interviewed 1,000 people between Wednesday and Friday, and has a 3.1 per cent margin of error.