(CNN) -- Costa Rican President Laura Chinchilla is urging citizens to exercise restraint as her government seeks a diplomatic course to resolve a boundary dispute with neighboring Nicaragua.
The neighboring Central American countries are in a dispute over a parcel of land on the Atlantic coast, along the San Juan River, known as Calero Island.
Costa Rica claims that Nicaraguan troops are camped out on the Costa Rican side of the border and it has asked the Organization of American States to intercede.
"Dear Costa Ricans: never before have we had to be united when the aggression and provocation test us," Chinchilla said in a televised address Wednesday night. "Let us be calm and firm, amid the outrage that these events provoke within us."
Costa Rica claims that its flag in the disputed area was taken down and replaced by a Nicaraguan flag.
Also, said Chinchilla, the Nicaraguans are destroying a forest in a protected area and a Nicaraguan dredging project in the river is dumping sediment on the Costa Rican side as well.
But, the president said, Costa Rica will respond "with prudence and sensibility."
"This is our strength," she said. "The strength of reason and not the strength of arms. We can't allow ourselves to get carried away by the profound indignation that this undeserved aggression causes us. Our tools are dialogue and international law, with those we are acting."
Costa Rica abolished its military after a 44-day civil war in 1948 that stemmed from a disputed presidential election and left more than 2,000 dead. It maintains only domestic police and security forces.
On Wednesday, the country called for an emergency meeting of the the permanent council of the Organization of American States in an attempt to resolve the spat. The body called a recess to discuss the matter further, and had not reconvened by Wednesday night.
"For the Costa Rican government, these actions constitute an unacceptable violation of its territorial integrity and sovereignty, and are absolutely indefensible by Nicaragua," Costa Rican Foreign Minister Rene Castro wrote in a letter to his Nicaraguan counterpart.
During his presentation, Castro showed slides with maps of the disputed area, arguing that Nicaragua's own maps show that the area in question is in Costa Rican territory.
He also showed photos showing the area where sediment was allegedly being deposited, and where the Costa Rican flag had been taken down.
Nicaragua said that an earlier judgment by the United Nations upheld its rights over the river area, although it gave Costa Rica freedom to navigate it. Nicaragua said that all of its activities are within its borders.
"We categorically reject the allegations made by Costa Rica," the country's ambassador to the OAS, Denis Moncada, said. "Nicaragua has not violated the sovereignty of Costa Rica. Nor is the dredging, in Nicaraguan territory, affecting Costa Rican land. With these statements, Costa Rica has broken the diplomatic equilibrium that traditionally exists between the two nations."
CNN's Catherine E. Shoichet contributed to this report.