At least 107,000 people turned out in Belgrade on Saturday, the interior minister reported.
Near-daily student protests began in December after the deaths of 15 people when a roof at a railway station collapsed on November 1 in the northern city of Novi Sad, which critics blame on corruption under Vucic.
Sporadic clashes occurred overnight before Saturday’s rally, in front of the National Assembly, from which protesters were to march to Slavija Square. Police deployed hundreds of officers in full riot gear in and around Pionirski Park and across the street.
Thousands of veterans from elite military brigades in maroon berets and bikers who support the students also stood for 15 minutes of silence beginning at 11:52am (10:52 GMT) to honour the victims of the Novi Sad tragedy at the time of the roof collapse.
Some protesters carried banners that read, “He’s Finished,” referring to Vucic. Others chanted, “Pump it up,” a slogan adopted during the four months of student-led protests.
“We came for justice. I hope that after this protest, things will change,” Milica Stojanovic, a biology student in Belgrade, told the AFP news agency before the demonstration.
While Saturday’s gathering is expected to be largely peaceful, on Friday night in the Zarkovo suburb, a car rammed a column of protesters, injuring three people, and police said they apprehended the driver.
In central Belgrade, a student and a university lecturer were injured in an attack by a group of men early on Saturday, police said.
Three people were also detained after an overnight attack on tractors stationed around Pionirski Park, they said.
In statements issued on social media on Saturday, students urged those attending the rally to act “in a calm and responsible manner”.
“The purpose of this movement is not an incursion into institutions, nor to attack those who do not think as we do,” one statement read. “This movement must not be misused.”
In a bid to avert tensions, students also said they had moved a stage at the centre of the planned protest from the front of the National Assembly building to Slavija Square, about 1km (0.6 miles) away.
So far, Serbian prosecutors have charged at least 13 people over the Novi Sad collapse, and the government has announced an anticorruption campaign. Prime Minister Milos Vucevic and two ministers have also resigned.
But pressure has been mounting in the days leading up to Saturday’s rally.
Government-backed media have broadcast increasingly harsh accusations, saying the students are planning to launch a “coup”. Earlier, Vucic himself accused the demonstrators of organising “large-scale violence”.
Vucic has warned of a “final” showdown on Saturday while some student protesters said they would continue to rally until their demands for greater accountability are met.
On Friday, Vucic took to the airwaves with a defiant message to demonstrators, promising to not back down in the face of mass protests.
