However, the 53-year-old leader does not intend to relinquish power in the country, despite massive protests that have gathered hundreds of thousands of critics in recent weeks. Vucic and the ruling party are accused of corruption and an increasingly authoritarian governance of the country.
The trigger for the extensive anti-regime demonstrations was two mass shootings in early May, one of which targeted an elementary school.
On Friday, Vucic called a large counter-demonstration in Belgrade where supporters showed their support for Serbia's leadership.
The decision to leave the party presidency, which was carried out at a televised party convention, is seen as an attempt to broaden the leadership within the party. '
Vucic, a founding member of the SNS party, has held leading positions in Serbia as president and prime minister since 2014.
The SNS party won a landslide victory in the parliamentary elections just over a year ago.