Indian Home Minister Amit Shah said he was "anguished" at the news of civilians, who were members of a local tribal group, being killed.
Nagaland's chief minister Neiphiu Rio told Reuters an investigation would be conducted and the guilty punished. He said the incident was the result of an intelligence failure.
India's northeast is home to a complex web of tribal groups, many of which have launched insurgencies, accusing New Delhi of plundering resources and doing little to improve their lives.
People in Nagaland have frequently accused security forces of wrongly targeting innocent locals in their counterinsurgency operations against rebel groups.
On Sunday, civilians launched protests against the government in the Mon district of Nagaland, where the 14 tribal people were killed.
"There is a mob outside which is pelting stones," a security official who did not want to be named told Reuters from the camp, which was surrounded by protesters.
"One civilian was shot dead and two more injured in firing by Assam Rifles a short while ago in Mon town," Noklem Konyak, president of the Konyak Students Union, told Reuters by telephone.
Konyak is the dominant tribe in Mon district.
Indian military and government officials were not immediately available to comment on the latest killing.
Saturday's incident took place in and around Oting village in Mon district, bordering Myanmar, during a counterinsurgency operation conducted by members of the Assam Rifles, the country's oldest paramilitary force, said a senior police official based in Nagaland.
Firing began when a truck carrying 30 or more coal mine labourers were passing the Assam Rifles camp.
"The troopers had intelligence inputs about some militant movement in the area and on seeing the truck they mistook the miners to be rebels and opened fire killing six labourers," the senior police official told Reuters, requesting anonymity.
"After the news of firing spread in the village, hundreds of tribal people surrounded the camp. They burnt Assam Rifles vehicles and clashed with the troopers using crude weapons," he said.
Members of the Assam Rifles retaliated, and in the second attack eight more civilians and a security force member were killed, the official said.
In recent years India has tried to persuade Myanmar to evict rebels from bases in the thick jungles of the unfenced region, which borders Nagaland, Manipur and Arunachal Pradesh.
(Reporting by Zarir Hussain; Additional reporting by Shilpa Jamkhandikar, Editing by Rupam Jain, William Mallard, David Evans and Alex Richardson) ((Rupam.Jain@thomsonreuters.com; +91 7042133028;))