"Nevruz should become a symbol of peace and fraternity," Davutoglu said in a statement Monday.
"Today, on this beautiful day, we -- as a nation -- should dignify the universal language of peace, love, and brotherhood, and also show that we are against all types of violence and terrorism," he said.
Nevruz marks the beginning of spring and has been celebrated in the Balkans, the Black Sea, the Caucasus, and most parts of Asia for hundreds of years.
This year celebrations in Turkey have been overshadowed by terror threats.
An explosion in Istanbul on Saturday killed five people, including the suicide bomber, three Israelis and an Iranian. Of the 39 injured, 24 were foreigners, including Irish nationals.
Local officials in the country's southeastern provinces of Mus, Batman, Bingol, Tunceli and Sirnak announced last week restrictions would be imposed on Nevruz celebrations due to security concerns amid counter-terrorism operations.
In Istanbul, at least 164 people were detained Sunday during unauthorized demonstrations to mark Nevruz, according to Turkish security sources.