The meeting comes a week after K P Sharma Oli government took charge in Nepal and reached out to Mahdhesis to resolve the imbroglio. India had expressed the hope that Prime Minister Oli will carry all sections of the society along so that there is peace and stability in that country.
Thapa apprised Singh about the prevailing situation in Nepal, which has plunged into a crisis following the blockade as supply of essential goods has been squeezed after the violent agitation in southern plains by Indian-origin Madhesis.
More than 40 people have died in clashes between police and the protesters.
The Madhesis and Tharu ethnic groups are protesting for more representation in the Constitution. They also see the model to split Nepal into seven federal provinces as flawed and discriminatory to their rights.
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Nepal had alleged that India has imposed an "economic blockade" on the country following the announcement of its Constitution. But India had rejected the allegation.
One of the main transit point at Birgunj bordering the Indian city of Raxaul has been blocked for over two weeks.
India on Thursday had decided to tighten security along its porous border with Nepal to check movement of Jehadi elements, smuggling of fake Indian currency notes and narcotics.
Of the 1,751 km long Indo-Nepal border, 263 km falls in Uttarakhand, 560 km in Uttar Pradesh, 729 km in Bihar, 100 km in West Bengal and 99 km in Sikkim.