"Our relations are not only of this world, but also of the 'other world' and they cannot be changed even if someone wishes so," he said at a BJP's virtual rally for Uttarakhand, the state in whose border region the road has been built.
"These are no ordinary ties and we are bound by 'roti' and 'beti' (livelihood and marriage). No power in the world can break it," Singh said.
The bilateral ties between the two countries came under strain after Singh inaugurated a 80-km-long strategically-crucial road connecting the Lipulekh pass with Dharchula in Uttarakhand on May 8.
Nepal's Parliament had on Saturday unanimously voted to amend the Constitution to update the country's new political map, laying claim over three strategically key areas, including Lipulekh, along the border with India.
"If the Lipulekh-Dharchula road has given rise to some misunderstanding among the people of Nepal, I believe we can sit together to address it. We can do it through dialogue," the defence minister said.
Singh, however, reiterated India's stand that the 80-km road had been built in Indian territory, while acknowledging that this had caused some misunderstanding in Nepal.
The road will shorten the duration of the Kailash Mansarovar pilgrimage by six days, according to Singh.
Nepal had reacted sharply to the inauguration of the road, claiming that it passed through Nepalese territory. India rejected the claim asserting that the road lies completely within its territory.
Nepal had last month released the revised political and administrative map of the country laying claim over the strategically key areas, more than six months after India published a new map in November.
At pains to highlight the deep ties between the two countries, the defence minister spoke about the valour of the Gorkha regiment, whose soldiers are mostly drawn from Nepal, and noted that its battle cry is "Maha Kali, Aayo Gorkhali" (Goddess Kali, Gorkhas are here).
"How can the India-Nepal relations be broken?" he asked. "No matter how much fencing one does across Dharchula, these ties cannot be ended," he said.
In his address, Singh also highlighted the work done by the Modi government and said it had delivered on a host of promises like abrogation of Article 370 and prohibiting instant triple talaq.
Gap between politicians' promises and their work had caused a "crisis of credibility", but the Modi government has triumphed over it by delivering on the party's manifesto, Singh said.
The government has also been working to reduce India's dependence on imports in the defence sector by boosting domestic manufacturing and exports of defence equipment. It has set an export target of USD 5 billion by 2024, he said.
According to Singh, India has progressed a lot under the six years of Prime Minister Narendra Modi-led NDA government and its economy had become fifth largest in the world from the ninth earlier.