Leung and Lam held a short press conference at the government house in central district minutes before a deadline set by students group which demanded Leung's resignation, Xinhua reported.
Thousands of protesters have blocked major roads in several districts in Hong Kong since Sep 28 to express discontent with electoral reform package for choosing the region's next leader.
Students issued an open letter asking for a meeting with the chief secretary
Students issued an open letter asking for a meeting with the chief secretary Thursday evening. Leung said the government studied the letter in detail. Carrie Lam said she wished to contact students as soon as possible to arrange the meeting, but neither she nor Leung gave a specific date.
Leung stressed that he would not resign, saying he will continue to work for promoting Hong Kong's constitutional reform which aims at universal suffrage to elect the region's next chief executive in 2017.
The chief executive said the Hong Kong Special Administrative Region (HKSAR) government and the police force have shown the greatest patience and endurance in the past five days.
Leung hoped that all circles in society could continue to carry forward the constitutional reform in a pragmatic, rational and peaceful manner.