The dispute has surfaced at a time when the process to elect new prime minister and form new government has formally begun Friday.
UML leaders are unhappy with Prime Minister Sushil Koirala for his refusal to announce his resignation from the post despite repeated request by the UML and UCPN (Maoist) leaders.
NC leaders meanwhile said the other parties need not pressure the prime minister as he has paved the way for election of new prime minister even without stepping down immediately.
"They should not have any problem as the prime minister has taken the initiative to create an environment both for forming new government as well as to take the agitating parties in confidence," said NC chief whip Chinkaji Shrestha. "So, the debate is unnecessary."
"The environment has improved in the last one week and we should not squander this opportunity to end the crisis," Shrestha told Republica.
Leaders from the major parties have also differed over whether or not the new constitution should be immediately amended to address the demands of the agitating political forces.
A cabinet meeting on Friday decided to begin the constitution amendment process. But the UML and UCPN (Maoist) leaders have expressed their strong objection to this decision.
"The bill to amend the new constitution can't be endorsed without an understanding among the three major parties. So we will discuss this matter again," said UCPN (Maoist) chief whip Giriraj Mani Pokharel.
UML and Maoist leaders have construed the prime minister's latest work as a result of the influence of some "interest groups and other elements" who want to break the unity among the major political parties.
They have also accused the prime minister of not sticking to the 16-point deal that envisioned continuity of collaboration of major parties in promulgation as well as in implementation of the new constitution.
"Those elements were hell-bent on breaking this alliance before promulgation of new constitution. They couldn't do so. Now they have tried to break the alliance at the time of implementation of the constitution," said UML lawmaker Rajan Bhattarai.
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