Top leaders of major political parties, including Prime Minister Sushil Koirala of the Nepali Congress, CPN-UML chairman K P Sharma Oli and UCPN-Maoist chairman Prachanda addressed the Constituent Assembly before the voting began.
Koirala said the major political parties are in their final efforts to promulgate a new Constitution with federalism, republic, democracy and inclusion.
"We will succeed in promulgating the new Constitution as we succeeded in resolving problems including through the comprehensive peace accord in the past," Koirala said.
Urging the disgruntled parties to engage in talks, Koirala said, "I call all the people not to have any doubt as consensus has been forged to move ahead with unity through the medium of talks, discussion, consensus and reconciliation.
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Some amendments could still be made even after promulgation of new Constitution if there are some weaknesses, he said.
Koirala urged the international community to extend support to the Constituting drafting process and expressed confidence that the international community will support the move.
Out of total of 598 valid members of the 601-member Constituent Assembly, only 538 are taking part in the Constitution voting process as 60 members of Madhesi parties are boycotting the sitting.
The Madhesi parties are protesting against the seven province model of the federal structure as proposed by the major political parties.
Southern Nepal has witnessed turmoil since lawmakers from major political parties struck a breakthrough deal on August 15 to divide the country into seven provinces. The protests have resulted in clashes between demonstrators and police, leaving 37 people, including policemen, dead.