The march came a day after student leaders said 13,000 students had taken part in a rally at a university campus.
They are protesting against a decision by Beijing to rule out fully democratic elections in Hong Kong in 2017.
Brief scuffles broke out as protesters rushed towards Chief Executive CY Leung as he left the government offices.
The Hong Kong Federation of Students claimed Mr Leung had ignored students and "simply walked past them".
RTHK quoted Mr Leung's spokesman who said he intended to accept a petition letter from the students but left when the situation became chaotic.
Mr Leung told reporters that he was willing to listen to protesters' requests, but stressed that Beijing had already made its decision and Hong Kong would still have a "one man one vote" electoral system.
The students' boycott is seen as a prelude to a larger demonstration planned for 1 October, organised by pro-democracy group Occupy Central, which has vowed to block the financial district.
In August, Beijing decided that candidates for the 2017 chief executive election would first have to be approved by a nominating committee. Activists have argued that this does not amount to true democracy.
State news outlet Global Times published an editorial on Tuesday saying activists were "misguided in their anger" and that Hong Kong had more important issues to deal with, such as growing inequality.
It said continued protests "benefits nobody, whether it be the activists, the public or relations with the mainland, and will accomplish nothing good for Hong Kong".
On Monday China's President Xi Jinping stressed that the "basic principle and policy" of "one country, two systems" towards Hong Kong "has not changed and will not change", according to Xinhua.
Q&A: Hong Kong's democracy controversy
More than 1,000 Hong Kong students have taken their pro-democracy march to government offices, as part of a week-long boycott of classes.