The soldiers, who were on a motorcycle patrol in Arauca, in eastern Colombia on the border with Venezuela, were gunned down by "terrorists of the ELN" traveling in a vehicle, the army said in a statement.
Reinforcements were rushed to the area to search for the culprits, the statement added.
The ELN is Colombia's second-largest rebel group after the Revolutionary Armed Forces of Colombia (FARC).
President Juan Manuel Santos and the FARC signed a peace accord on November 24 to end five decades of warfare, after a first agreement was unexpectedly rejected by Colombians an October 2 referendum.
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The Colombian government has suspended the preparatory talks until January 10, insisting that the ELN first release hostage ex-congressman Odin Sanchez.
The ELN in turn called for the simultaneous release of two imprisoned rebels.
More than 260,000 people have died in Colombia's decades-long conflict, which drew in other guerrilla forces, right-wing paramilitary groups, drug traffickers and government troops.