"We have never recognised the so-called Arunachal Pradesh illegally established on the Chinese territory", Chinese Foreign Ministry's Spokesperson Zhao Lijian said during his regular briefing.
Relations between the countries have steadily deteriorated in recent months.
The allegations of firing, if true, would be the first time in 45 years that shots had been fired there.
This time the Chinese reaction comes at a time when the Defence Ministers of two sides met in Moscow to ease up the tensions between the two countries on the Line of Actual Control (LAC) in Ladakh.
Terming the move a grave military provocation, Zhang said: "The flagrant act grossly violated the agreements previously reached between the two sides, and further escalated regional tensions, which can easily lead to misunderstandings and misjudgments".
The PLA Western Theater Command troops will firmly fulfill duties and missions and resolutely safeguard national territorial sovereignty, Zhang said.
The PLA spokesperson also called on the Indian side to "immediately stop risky moves, withdraw personnel who crossed the LAC. and punish the personnel who fired the provocative shot".
China called on India to strengthen control of its frontline forces, refrain from provocative actions and "refrain from deliberately hyping and disseminating negative information".
Union Minister Kiren Rijiju responded to a journalist's tweet on Sunday asking about the update on the five Indians that are reportedly abducted by the PLA. Asked whether Russian Federation will consider exporting weapons to Pakistan, he said "it is based sensitivities of the Indian side", virtually ruling out such a possibility.
The Indian Army has now changed the rules of engagement after the Galwan Valley clash on June 15 where Chinese used improvised weapons including iron rods studded with nails to attack Indian soldiers. Local media outlets said then that the soldiers had been "beaten to death".
Apart from fighting a war in 1962, India and China have largely resolved flare-ups along their 2,200-mile border through dialogue. On the contrary, India has said that the current stand-off was triggered due to China not adhering to the bilateral agreement on informing each other on the nature of military exercises near the LAC.
The soldiers on either side - representing two of the world's largest armies - come face to face at many points. "We are focusing on the creation of a positive atmosphere for it", Babushkin said, ruling out the possibility of Russian Federation playing the role of a mediator unless it is asked to do so by both India and China.
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