The farmers, who launched their protest Monday, complain that free-trade agreements with Europe and the United States are flooding the country with cheap food imports, exacerbating rural poverty.
Defense Minister Luis Carlos Villegas announced the "death of two indigenous persons during the day's protests" in a tweet.
In a subsequent posting, he said there was no evidence yet that the deaths were the result of police action.
The National Indigenous Organization of Colombia (ONIC) said the two victims were from the western department of Cauca and died from gunshot wounds.
The Defense Ministry reported that 31 members of the security forces were injured.
The farmers accuse President Juan Manuel Santos's government of breaking its promises to them, and are demanding land reform and increased state spending in rural areas.
Protests have now erupted in 24 of Colombia's 32 departments, shutting down at least 14 roads, the government rights ombudsman's office said.
Police have broken up 11 other roadblocks, in some cases sparking clashes.
The key Pan-American Highway was cut off in several spots by farmers wielding sticks and stones.
Interior Minister Juan Fernando Cristo traveled yesterday to the department of Cauca, where one of the largest protests was being held, to try to broker a deal for negotiations.
Rural poverty and land tenure are explosive issues in Colombia, where peasant uprisings more than half a century ago morphed into an armed conflict that is still ongoing.
The conflict, which has drawn in leftist guerrilla groups, right-wing paramilitaries and drug gangs, has killed 260,000 people.