"Considering the current crisis facing the nation and the public necessity and aspirations, the ongoing protest programmes of general strike, border blockade, government office shutdown have been called off for now," the United Democratic Madhesi Front (UDMF) said in a statement.
"The agitation will continue till our demands are addressed," said the statement issued after the meeting of UDMF leaders, three days after angry traders from both sides burned down tents set up by agitating Madhesis on Friday.
The announcement to end the border blockade comes ahead of Prime Minister K P Oli's trip to India on February 19, the first overseas visit of the new Nepalese premier.
Prime Minister Oli welcomed the decision by the Madhesis to call off the agitation and said it was a "positive move."
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"The Prime Minister has stressed on talks among the parties to address the differences," said a press note issued by Oli's press advisor.
Nepal's Madhesi community, largely of Indian origin, are opposed to the new Constitution that divides their ancestral homeland under the seven-province structure and have led an ongoing blockade of key border trade points with India.
The blockade had caused much hardship to the general public as they were faced with acute shortage of petroleum products, cooking gas, medicines and other essentials due to closure of all border trade points between the two countries.
The blockade led to strain in the bilateral ties, with Kathmandu accusing New Delhi of imposing an "unofficial blockade".
However, India maintains that it has imposed no such blockade, and the restrictions are a result of security concerns as Madhesis are protesting the new Constitution in the Terai region of Nepal bordering India.
Karna said that the UDMF is considering to change forms of their protests.
Madhesi community, Nepal's parliament last month voted to amend the new Constitution four months after its promulgation.
However, the Madhesi groups rejected the two amendments, saying that they did not address their demands.
The amendment addressed two demands of the Madhesis - proportionate representation and seat allocation in the Parliament on the basis of population.
However, their key demand on the re-demarcation of the provincial boundary is yet to be addressed.
The major political parties have pledged to address their demand related to the boundary demarcation through setting up a high-level political committee.
The alliance has called for forging a broader coalition with other political parties for their future programmes.
The UDMF has also raised objection to what it called the "government's premeditated attempt" to spread false message that the agitating forces were defeated.
The Morcha is determined that it won't back down from its struggle under no circumstances, the front said.