Singh said the government is showing flexibility to draft the constitution through consensus among political parties.
But if consensus could not be achieved on contentious issues, the new constitution would be promulgated through two-third majority as per the provisions of the Interim Constitution, he said.
The Nepali Congress general secretary stressed that a lack of consensus would not become an excuse for not drafting the constitution.
Opposition parties led by UCPN-Maoist demand an ethnic identity-based federal structure in the new Constitution, which was initially supposed to be promulgated by January 22.
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Communist Party of Nepal (Unified Marxist-Leninist) chairman K P Sharma Oli has, however, said his party is committed towards forging a consensus among political parties.
"We want to draft a constitution through consensus or agreement among political parties and the new constitution should be promulgated taking into account peace and stability as well as national unity and integrity," said Oli.
The constitution should be drafted at the earliest so that Nepal could move forward on the path of economic prosperity and development, Oli said at a programme organised by the World Federation of Trade Union in Kathmandu.
Top leaders of ruling parties, Nepali Congress and CPN-UML have been trying to persuade the 19-party opposition alliance to break the logjam on the constitution drafting process.