Hundreds of trucks loaded with essential goods, cooking gas cylinders and petroleum products were stalled at the Nepal-India border due to the agitation.
The protesters belonging to the Joint Madhesi Front were opposing the provision in the new Constitution that divides the country into seven federal provinces.
The agitating Madhesi Front claims that the Constitution does not guarantee enough rights and representation to the Madhesi and Tharu communities residing in southern Nepal.
At least 40 people have died in over a month of clashes between police and protesters from the Madhesi and Tharu communities and ethnic minorities who say the new internal borders leave them under-represented in the country's Parliament.
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The blocked checkpoint in Birgunj which lies 200 km south of the capital, serves as a major transit point between Nepal and India.
Although the shutdown in the region was lifted temporarily today due to the Muslim festival of Eid-ul-Azha, the blockade continued at the Nepal-India border check point affecting normal life.
According to reports, the leaders told Ambassador Rae that the two nations should improve their relations and the problems of Nepal should be dealt by Nepali leaders themselves.
The leaders also drew Rae's attention to the crisis at the entry points to Nepal from India where Nepal-bound cargo and freight have been left stranded at the Indian side of the border and has allegedly not been given clearance.
Rae stated that the problems were not created due to India. He said the obstruction was caused by the protests in Nepal's Tarai/Madhes region.