Several police vehicles were blocked by protesters, and riot police moved in, pushing some protesters back and using pepper spray at times amid heated scenes.
Protesters also barricaded some passageways in the airport with luggage trolleys and other objects.
Hong Kong’s Airport Authority said operations at the airport had been “seriously disrupted” and that departing passengers had been unable to reach immigration counters.
Hong Kong’s stock market fell to a seven-month low.
President Trump addressed the situation in Hong Kong in a pair of tweets Tuesday.
The weeks of protests began as opposition to a now-suspended bill that would have allowed suspects to be extradited to mainland China, but have swelled into wider calls for democracy.