Sunday's march was the latest major protest calling for the full withdrawal of the legislation, which would have allowed the transfer of fugitives to mainland China and other jurisdictions with which the city had no extradition agreement, reports the South China Morning Post.
Protesters are aiming to take the march to the high-speed train station in western Kowloon, which operates a service connecting Hong Kong to the mainland Chinese cities of Guangzhou and Shenzhen.
Shortly before the march, organiser Ventus Lau Wing-hong said he believed more people had joined in solidarity with protesters who had stormed the legislature on July 1.
"I believe the residents who came out today want to tell the government that they are united and won't be split," he added.
He appealed to the marchers to "remain peaceful and graceful" in the face of heavy police presence and possible provocation from members of the opposite camp.
Crowds had responded to his call with applause and a loud chorus of "yes".
To avoid any potential disruption, police stepped up their presence around West Kowloon and Tsim Sha Tsui, and some officers carried pepper spray as they patrolled Salisbury Road near the Hong Kong Cultural Centre.
Sunday's protest march comes after a group of Hong Kong student leaders last week rejected Lam's offer of a private meeting about the recent protests over the now-suspended extradition bill, calling it "too little, too late", the South China Morning Post reported.
The government's offer came after hundreds of mostly young protesters stormed the city's legislature on the night of July 1, writing slogans on the wall, defacing Hong Kong's official emblem and smashing equipment, furniture and work areas.
Among the protesters' demands were for Lam to fully withdraw the bill and to order an independent inquiry into the use of force by police during clashes on June 12.
( With inputs from IANS )