Leung, speaking just minutes before an ultimatum for him to resign expired, also said that Chief Secretary Carrie Lam would hold a meeting with students soon to discuss political reforms. He gave no specific time frame.
"I won't resign because I must carry out the universal suffrage work," said Leung, referring to electoral reforms in the former British colony.
In August, Beijing ruled out free elections for the city's next leader in 2017, triggering mass protests that saw students storm government buildings a week ago and police fire tear gas to disperse them on Sunday.
Leung appealed to the protesters to exercise restraint.
"In any place in the world, if there are any protesters that surround, attack, or occupy government buildings like police headquarters, or the chief executive's office ... the consequences are serious," he said.
Hong Kong authorities had earlier urged thousands of pro-democracy demonstrators to immediately end their blockade of the city centre. The protests, nearly a week old, have brought large parts of the Asian financial hub to a standstill.
The protesters remained calm after Leung's address, although many were dissatisfied and said his comments were not enough.
"I don't think this is sufficient. I think he's trying to slow down the process and make us go home ... (but) people are feeling tired, mentally and physically and the numbers may decrease," said Nicholas Chan, 20, a journalism student at Chinese University.
"The bargaining power is in the numbers."
