The semi-autonomous region currently has a chief executive, selected by about 800 mostly pro-Beijing officials.
Hung said that 20,000 people, including religious, political and civil leaders, were expected to march.
Police said that at first count about 6,800 people had marched.
Universal suffrage has been promised to the former British colony under the Basic Law when its administration was passed to China in 1997.
The law stipulates that an electoral process should be in place by 2007.
China, which maintains the right to final say on any political reforms in Hong Kong, says that the financial centre does not have the political maturity needed to directly elect its representatives.
Analysts have argued that Beijing is reluctant to allow democracy in Hong Kong for fear of its influence in mainland China.
Relations are also said to be strained by criticism of human-rights abuses in China by Hong Kong's pro-democracy activists and legislators.
Thousands of the city's 6.9 million people also gather every June 4 to commemorate the deaths of hundreds of democracy activists by the Chinese military in Tiananmen Square in 1989.
China is scheduled to take over full control of Hong Kong in 2047.
Hong Kong is one of Asia's most sophisticated and affluent societies.
It has free significant financial, political and personal liberties - such the right to hold protests and criticise the government - not available to mainland Chinese citizens.