The students are facing a showdown with Beijing over its decision to rule out fully democratic elections for Hong Kong's next leader in 2017, with about 13,000 joining a rally at a university campus on Monday to mark the start of a week-long boycott of classes.
The ultimatum came after scuffles broke out when the students took their pro-democracy protest to government headquarters, where they pushed through barriers and rushed to meet Hong Kong leader Leung Chun-ying as he stepped out to meet the crowd in the Central business district.
Leung did not speak to the students but told reporters that any political reform would need to take into account Beijing's wishes.
"If he doesn't come to the community in 48 hours to have direct dialogue with the students and the people, and answer people's questions, then we will definitely escalate the movement," said Hong Kong Federation of Students leader Alex Chow, 24.
The students urged Leung to join them on a protest stage, reserving a chair for him to step up and address them, and threatening further action if he did not respond. They did not elaborate.
The Federation of Students said about 4,000 people had turned out to protest near the heart of Hong Kong's financial district on Tuesday.
Hong Kong returned to Chinese rule in 1997 with a high degree of autonomy and freedoms not enjoyed on the mainland under a formula known as "one country, two systems".
But Beijing last month rejected demands for people to freely choose the city's next leader in 2017, insisting that candidates had to be pre-screened, prompting threats from pro-democracy
activists to shut down Central.
"We will pay full attention to the views of all sectors of the community," Leung said. "...all proposals to implement universal suffrage to elect the chief executive in 2017 have to be within the framework of the Basic Law and also the relevant decisions of the National People's Congress."
The Basic Law refers to the mini-constitution for post-1997 Hong Kong which enshrines the one country, two systems formula. The National People's Congress in China's parliament.
This week's student boycott of classes is the latest in a string of civil disobedience campaigns in Hong Kong which has been dogged by a series of rallies over the issue of electoral reform.
Monday's protest was peaceful but the mood was defiant at the university, where a black cloth was draped over a replica statue of the Goddess of Democracy, which Chinese students rallied around during a bloody crackdown on pro-democracy students in Beijing's Tiananmen Square on June 4, 1989.
The students' ability to mobilise thousands to fight for democracy has made their support an increasingly important driver of the city's burgeoning civil disobedience movement.
For Beijing, the prospect of protracted student protests highlights one of their worst fears - a student movement that spreads across the mainland, challenging the Communist Party's grip on power.
Many university professors on Tuesday were delivering lectures on democracy, universal suffrage and civil disobedience in a Central park as students sat on the grass.
"When the teachers voluntarily give us lessons here, we can absorb the knowledge better," said second-year Chinese University of Hong Kong student Steve Cheung, who was wearing the protest trademark white shirt and yellow ribbon and seated near a banner reading "Disobey, Boycott."
Organisers were holding various seminars throughout the evening, including lectures and showing displays of major political events in Hong Kong.
A handful of secondary students also made an appearance ahead of Friday, when they are officially expected to join the protest.
"I am not scared. I am prepared to accept any consequences for my absence," said one 16-year-old who skipped school.