The government stepped down on October 29 but stayed on in a caretaker capacity as no overt efforts have been made to form a new one.
Dozens of protesters gathered near the Palace of Justice in central Beirut on Tuesday morning, demanding an independent judiciary, an AFP correspondent said.
They tried to prevent judges and lawyers from going to work, as a demonstrator in a panda suit made an unusual addition to the protest.
In the town of Aley east of Beirut, in the southern city of Tyre, and the eastern town of Baalbek, demonstrators held sit-ins outside - or inside - the offices of the state telecommunications provider, local media reported.
Employees at the two main mobile operators, Alfa and Touch, started a nationwide strike.
Many schools and universities were closed, as were banks after their employees called for a general strike over alleged mistreatment by customers last week.
The union of banks on Tuesday said they were striving to ensure safe working conditions so employees could return to work as soon as possible.
Banks have restricted access to dollars since the start of the protests, sparking fears of a devaluation of the local currency and discontent among account holders.
The central bank on Monday however insisted the Lebanese pound would remain pegged to the dollar and said it had asked banks to lift restrictions on withdrawals.
Students, who have emerged as key players in the uprising, held further demonstrations later in the day.
An interview with the president was to be broadcast in the evening, after he met foreign ambassadors and the UN's special coordinator for the country, Jan Kubis.
The UN envoy urged Lebanon to accelerate the formation of a new government that would be able "to appeal for support from Lebanon's international partners". "The financial and economic situation is critical, and the government and other authorities cannot wait any longer to start addressing it," he said.