"There has been important progress in Tunisia's transition," Moon said in a statement issued Friday. "Yet, much remains to be done in terms of the constitutional process and with regard to meeting the social and economic demands of the Tunisian people."
Belaid, 48, secretary-general of the Democratic Patriots Movement and one of the leaders of the Popular Front in Tunisia, was assassinated Wednesday in front of his home in Tunis.
His burial was Friday, declared a national day of mourning.
Sporadic protests and clashes have been reported around the country since the killing.
Earlier this week, U.N. High Commissioner for Human Rights Navi Pillay called on authorities to investigate the assassination and other apparent politically motivated crimes, and to provide better protection for people who are political targets.
Thousands of mourners gathered in the Tunisian capital Friday for the funeral procession and burial of Belaid.
Witnesses said the atmosphere in Tunis was calm, in part because authorities decided to have a light military presence rather than a police contingent that could have incited protest, Britain's Guardian reported.
President Moncef Marzouki said flags throughout the country would be flown at half-staff Friday.
The funeral procession began in Djebel Jelloud, the Tunis suburb where Belaid grew up, and ended at El Jallaz cemetery for his burial in Martyr's Square, Tunisia Live reported.
Contrary to Tunisian traditions, Belaid's wife, Besma Khalfaoui, called on women to participate in the procession to the cemetery.
Tunisia's largest labor union called for a general strike nationwide Friday to coincide with the funeral.