Martin Kobler, U.N. Secretary-General Ban Ki-moon's special representative in Iraq, issued his call in a news release from the U.N. Assistance Mission in Baghdad.
"We call on the protesters to refrain from violence and to maintain the peaceful character of their demonstrations and on the security forces to show the utmost restraint in maintaining law and order," Kobler said.
Kobler called for "peaceful and constructive" dialogue.
In recent weeks, thousands of Sunni Muslims have taken to the streets to protest the government of Prime Minister Nouri al-Maliki. While Maliki's officials come from all sectarian and ethnic groups, it is dominated by Shiite Muslims.