The protest group also wants the resumption of public consultation on democratic reforms.
Thousands of protesters are camped outside government headquarters in central Hong Kong.
Occupy Central leader Benny Tai announced the launch of the campaign to the cheers of supporters on September 27.
A statement said that Hong Kong Chief Executive CY Leung had “failed to deliver on political reform”.
“We demand CY Leung deliver a new report on political reform to the central government, which must adequately reflect the demands of Hong Kong people for democracy,” it said.
“If CY Leung does not respond, we will escalate our actions.”
The movement had originally planned to paralyze the central business district on September 24, but organizers brought forward the start of the protest and changed the location in an apparent bid to harness momentum from student protests outside the government complex.
Student activists had stormed into a courtyard of the complex late on September 26 and scuffled with police using pepper spray.
Police said they made scores of arrests including prominent student activist leader Joshua Wong.
However, some students expressed unease that their protest was apparently being taken over by Occupy Central.
The protests at government headquarters followed a week-long strike by thousands of students.
Unrest began when the Chinese government announced 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.
Many of those who spent the night on the streets wore plastic raincoats and goggles in case police deployed more pepper spray.
Riot police stood nearby.
“The courage of the students and members of the public in their spontaneous decision to stay has touched many Hong Kong people,” Occupy Central said in a statement.
“Yet the government has remained unmoved. As the wheel of time has reached this point, we have decided to arise and act.”
At least 34 people have been injured since the protests began, including four police officers and 11 government staff and guards, authorities said.
One police officer suffered a gash after being poked by one of the umbrellas protesters are using to deflect pepper spray.
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