Erdogan says Turkish citizens are free to live according to their own culture, religion and traditions.
In a statement, Recep Tayyip Erdogan especially wished the Turkish Jewish community, adding that the occasion marks one of the most important feasts of the religion.
"We believe it is a fundamental right of all our citizens to live in accordance with their own culture, religion and tradition," Erdogan said.
He said the government attached great importance to an atmosphere of peace for its citizens, so that they live freely without being subjected to religious, ethnic and linguistic discrimination.
According to the Jewish faith, Rosh Hashanah marks the creation of Adam and Eve, the first man and woman on earth.
Close to 18,000 Jews live in Turkey, mostly centered in Istanbul, media reports state.