But Mrs. Lam unexpectedly acknowledged that broader, fundamental issues lay beneath the demonstrations, issues that emerged during a failed protest movement in 2014 that sought fully democratic elections for the city’s leader.

The protesters’ forceful occupation of the legislature on July 1 was a stark rebuke of Mrs. Lam’s administration, and of what many protesters consider the political system’s failure to prioritize Hong Kong’s interests over those of the Chinese government. In recent days, the protesters have expanded their demands to include the right to directly elect the city’s leadership, as well as other political reforms.

While Mrs. Lam pointed mainly to economic issues in her remarks on Tuesday, Ronny Tong, a lawyer and a member of the territory’s Executive Council, or cabinet, said in an interview that he believed “she does understand that one of the core areas of divide within the community is about political reform.”

Concerns have grown in Hong Kong about Beijing’s interference in the territory’s political system, which has resulted in a number of major setbacks for the pro-democracy camp. Six elected lawmakers were removed from office and several others were disqualified from running in local elections.

Joshua Wong, a key figure from the 2014 movement, and Eddie Chu, a pro-democracy lawmaker, staged a small demonstration on Tuesday to raise concerns about the possible disqualification of pro-democracy candidates in district elections set for November.

While Mrs. Lam’s comments were her strongest attempt yet to reassure the public that the government had learned its lesson from the bungling of the extradition bill, experts said the effort was unlikely to quell widespread anger. For some, the argument over the formal status of the bill has become a proxy for a larger debate over Beijing’s influence within Hong Kong’s political system.