Jeffrey Feltman, UN Under-Secretary-General for Political Affairs, asked the politicians write a new constitution that is based on a broad consensus and inclusiveness.
"We encourage political leaders in Nepal to put aside their narrow interests and exercise flexibility in reaching an agreement in the interest of all the Nepali people," he said.
"There are risks of confrontation and conflict," said Feltman.
"It is our firm belief that only Nepalese can take the important political decision that are needed for the full implementation of the Comprehensive Peace Agreement of 2006," he said.
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"I strongly encourage the leaders to neither threaten to a walkout nor force a vote, but rather to conclude the process through compromise, flexibility and inclusiveness," he said.
Feltman expressed UN's long-term commitment to Nepal's development and democratic stability.
He said it is essential for political leaders to seize the opportunity and carry out the mandate entrusted to them by the people of their country.
The stability the constitution can provide is the key for prosperity, he observed.
"Adoption of the constitution will be the culmination of Nepal's historic peace process."
The political parties are sharply divided on key issues such as forms of governance, federal structure and electoral system, ahead of the January 22 deadline to promulgate a constitution.
Feltman also called on President Ram Baran Yadav and Prime Minister Sushil Koirala during his two-day official visit to Nepal, according to sources at the UN office in Nepal.