The demonstrators cited allegations against C.Y. Leung, who enjoys Beijing's support, about illegal structures in his home, while also pressing for democratic rights to enable them to vote for their leader, the BBC reported.
The report said police estimated the number of protesters was about 26,000 while the organizers said the number was at least 130,000.
Hong Kong's Victoria Parka was one of the several places on the island where the anti-Leung protests were held, the BBC reported.
The New York Times reported there were also simultaneous pro-Leung rallies, which pointed to the political differences existing in Hong Kong, which Britain ceded back to China in 1997. Tuesday's demonstrations were largely peaceful, it said.
Though under Communist China, the territory enjoys much autonomy because of its strong economy and financial stability which attracts considerable foreign investments. Leung has been in office since last July.
Opponents of Leung say the chief executive has misled the people on the renovations to his home and of being a puppet of China.
Leung's supporters say he seeking to address the major social issues on the island. The Times said some supporters also seem to indicate democracy as a Western concept may not suit the local culture.
The BBC quoted organizers of the pro-Leung demonstrations as saying there were about 60,000 people but that police estimated the number at about 8.500.
The BBC report said some of the anti-Leung banners and posters showed the chief executive as Pinocchio or a wolf. Some protesters also carried British colonial-era flags.
Any issue related to real estate can get touchy because of the limited living space in Hong Kong.
Local media reports said some of the protesters remained at one of the sites on Wednesday, vowing to continue their action until Jan. 16 when Leung his scheduled to make a deliver a policy address.
The New York Times quoted police Wednesday that nine anti-Leung protesters had been arrested for disorderly conduct and unlawful assembly after they tried to cross police lines to protest at the front gate of Leung's residence.
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