Ecuadorean President Lenín Moreno has confirmed the death of two journalists and their driver who were reportedly abducted by Colombian rebels.
Javier Ortega, Paul Rivas and Efraín Segarra are believed to have been seized by a dissident faction of the disbanded Farc rebel group.
An emotional Mr Moreno said in a televised address the country would not "let ourselves be intimidated".
He promised to resume military operations on the border.
He also promised a reward for information about the rebel leader.
Colombian President Juan Manuel Santos earlier said Ecuador could rely on his country's armed forces for support.
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The three men, who worked for Ecuador's El Comercio newspaper, were taken near the village of Mataje on 26 March.
Mr Ortega was a reporter and Mr Rivas a photographer, while Mr Segarra was their driver.
Mr Moren promised a $100,000 (£70,000) reward for information about the dissident Farc group's leader, known by the alias Gaucho.
"We can't allow the criminals to impose their rules," Mr Moreno said on Thursday, adding "We're going to fight them in the realm they have chosen and we are going to defeat them."
More than 1,000 former Farc rebels are thought to have joined dissident drug-trafficking groups since the landmark peace deal between the rebels and the Colombian government.
Drug traffickers and rebel forces operate on the Ecuador-Colombia border, and have launched a number of attacks on military targets.
President Moreno announced plans in March to send 12,000 soldiers and police to the region to combat the gangs.