Troops from both sides have been facing off in the remote Himalayan region of Ladakh since early May when a long-running territorial disputes boiled over. The situation quickly escalated with tit-for-tat accusations of trespass and in recent days both sides have started to dig in defences and deploy military equipment.
Mr Trump announced on Twitter he had told India and China he was ready to arbitrate their “raging border dispute”, the first time he has tried to throw himself into India-China diplomacy.
But neither side has taken the US President up on his offer and India insisted talks between Beijing and New Delhi were already underway.
Indian Foreign Ministry spokesman Anurag Srivastava said: “We are engaged with the Chinese side to peacefully resolve this issue.”
Mr Srivastava said India wanted peace and stability at the border but warned it would defend its territory.
China has not yet made an official comment.
The border clashes are the most serious since India and China were locked in a similar stand-off in the eastern Himalayas that lasted nearly three months in 2017.
Despite talks spread over two decades, the two countries have not been able to agree on their 2,175-mile border and lay claim to large tracts of remote territory in each other’s possession.
Mr Srivastava said: “Our troops have taken a responsible approach towards border management and are following protocols.”
Military observers say one likely reason for the renewed border tensions is India’s effort to build new air strips and roads near the de-facto border to try to narrow the gap with China’s superior infrastructure.
Indian sources said there was no sign of a de-escalation despite ongoing talks between the local military commanders and diplomats.
New Delhi says Chinese troops have intruded into Indian territory and must withdraw to defuse the crisis.
The Chinese side wants India to stop all construction activity in the area, saying the whole area is disputed.
Tensions boiled over into violence on May 5 when PLA officers objected to Indian military patrols in the area.
And on May 9 in the Naku La region near Tibet, soldiers from both sides came to blows and threw stones at each as PLA soldiers tried to force Indian troops back from their positions.
According to reports, no weapons were fired but several dozen soldiers were injured, including a senior Indian officer who was required to be airlifted to a hospital.