The area, known as Kalapani, was shown in the new maps released on the occasion of bifurcation of J&K into two UTs last month.
Kalapani, located 18 km from Lipulekh pass, is a transit route for the Kailash-Mansarovar yatra and the Indo-Tibetan Border Police.
Nepal Prime Minister K.P. Oli on November 17 said the Kalapani area belonged to Nepal and India should "immediately withdraw its Army from there".
"We will not allow even an inch of our territory to be occupied by any country; India must vacate it," Oli said, adding that dialogue with India will follow after "India withdraws its Army from our land".
India has said that the new map "accurately depicts the sovereign territory of India" and that it has not revised the boundary with Nepal.
"The new map has in no manner revised our boundary with Nepal. The boundary delineation exercise with Nepal is ongoing under the existing mechanism," the Ministry of External Affairs spokesperson Raveesh Kumar said earlier this month.
"We reiterate our commitment to find a solution through dialogue in the spirit of our close and friendly bilateral relations," Kumar said. He also said that both sides should "guard against vested interests trying to create differences between our two countries".
Meanwhile, Uttarakhand Chief Minister Trivendra Singh Rawat on Tuesday said the Kalapani area is an integral part of India.
"This is an unfortunate statement by the Nepal government, and not in keeping with its culture. Kalapani is an integral part of India and will remain so. I hope the matter will be defused through talks," Rawat is quoted as saying.
Kalapani is located at an altitude of 3,600m on the Kailash Manasarovar route. It borders Uttarakhand in India and Sudurpashchim Pradesh in Nepal.
Since 1962, Kalapani has been manned by the Indo-Tibetan Border Police.
Under the Treaty of Sugauli signed between Nepal and the British East India Company in 1816, the Maha Kali river was located as Nepal's western boundary with India.
The treaty made no mention of a ridgeline and subsequent maps of the areas drawn by British surveyors showed the source of the river at different places.
Nepal claims that the river located towards the west of the territory is the main Maha Kali river and thus it falls in its territory, India claims the ridgeline towards the east of the Kalapani territory, and hence includes it in the Indian Union.
Both the countries have been producing maps, including the territory in their own area, to support their claims.
( With inputs from IANS )