Serbia's President Aleksandar Vucic said the country would hold snap parliamentary elections, amid ongoing protests following two incidents of gun violence.

He said it is clear that early parliamentary elections will be held but did not announce a date.

After Prime Minister Ana Brnabic resigns from the assembly, he must offer the mandate to someone else within the next 30 days, he said.

"This means that we are soon going to dissolve the Serbian parliament because there are deadlines," said Vucic.

"When it is established that there is no majority in the Assembly of Serbia, if there is none, it is possible for someone else to make the majority, if it turns out that this is not possible, since if Ana Brnabic resigns, the Serbian Progressive Party will not want a new mandate, it is understandable."

The snap elections would mean voters will head to the polls for the third time in four years.

Vucic and the government were under pressure in recent weeks after two mass shootings in the national capital of Belgrade.

Thousands were protesting on the streets, demanding Vucic's resignation.

The opposition protesters have been demanding the resignations of senior government officials and the revocation of broadcasting licenses for two pro-government television networks which, they say, promote violence and glorify crime figures.

A new protest is planned for this weekend in what is becoming an increasingly serious challenge to Vucic, perhaps the biggest one he has faced since coming to power 11 years ago.

The two shootings on May 3 and 4 stunned the nation, because the first one happened in an elementary school in central Belgrade when a 13-year-old boy took his father’s gun and opened fire on his fellow students. Eight students and a school guard were killed and seven more people were wounded. One more girl later died in hospital from head wounds.

A day later, a 20-year-old used an automatic weapon to randomly target people in two villages south of Belgrade, killing eight people and wounding 14.