India and China have long been embroiled in a bitter border dispute at both ends of the Himalayas, with the two countries accusing soldiers of crossing over into the other's territory.
"Our position to uphold our territorial sovereignty is unwavering," spokesman Lu Kang told a regular briefing, adding China has lodged "solemn representations" with India.
"We hope that the Indian side can work with China in the same direction and take actions to withdraw the personnel who have overstepped and trespassed into Chinese borders."
A statement posted on the Chinese defence ministry's social media account offered few details about the alleged incident, but said it had "seriously endangered peace and tranquility in the border areas".
The Indian military has "unilaterally stirred up trouble" by obstructing road building activities on the Chinese side of the border separating Sikkim and the Tibetan region, it said.
In apparent retaliation, China has blocked Indian pilgrims from crossing the border in the mountainous area "out of security concerns", the Chinese foreign ministry said.
"For the upcoming actions we have to depend on what the Indian side will do. They have to take actions to improve the security situation," the foreign ministry's Lu said.
Indian media said China had turned back 50 pilgrims trying to cross into Tibet to visit a mountain revered as the home of the Hindu god Shiva. Authorities there normally allow the annual pilgrimage to go ahead.
India's foreign ministry spokesman said last week the pilgrims had experienced "some difficulties" in movement and these were under discussion with Beijing.
In an earlier statement, China's foreign ministry called on India to "immediately withdraw their border troops that have crossed the boundary, conduct a thorough investigation into this and safeguard peace and tranquility of the Sikkim section".
Tensions along the frontier rose in 2014 when Chinese soldiers moved into territory claimed by India, sparking a two-week military stand-off.
Hundreds of Indian and Chinese troops faced off on the de facto border known as the Line of Actual Control, which runs along the remote mountainous region of Ladakh in northwest India, overshadowing a visit by China's President Xi Jinping.
The neighbours, now nuclear-armed, fought a brief but bloody war in 1962 over the Indian state of Arunachal Pradesh in the eastern Himalayas, and are still embroiled in a bitter dispute over the territory.
Aside from the festering border issue, China's close ties with India's archrival Pakistan, where it is pursuing a slew of infrastructure projects, has also been a source of tension.
