Rupert Colville, a spokesman for the U.N. Office of the High Commissioner for Human Rights, said the world body was following the "extremely tense situation" in Egypt with "great concern."
Morsi brushed off a military ultimatum to find a way to address renewed political unrest in the country. The military said Morsi had to find a way to resolve the crisis by midweek or the country's leading generals would take unilateral action.
A military council ruled Egypt after the 2011 revolution and before Morsi was elected in June 2012 in Egypt's first democratic election in history.
Colville said the United Nations supported the aspirations of the Egyptian people but said all sides needed to resolve their political differences peacefully.
"We urge all political parties and social groups to urgently engage in a serious national dialogue in order to find a solution to the political crisis and prevent an escalation of violence," he said in a statement from Geneva.
Morsi's administration has faced criticism for pursuing a conservative Islamic political ideology. An economic crisis in Egypt is compounding the national security situation.