HONG KONG — Pro-democracy student leaders will sit down for their first formal talks with government officials in Hong Kong on Friday, yet they have almost no hope of finding a solution to end the protests that have both inspired a generation to fight for political change and divided opinion in the city where they live.

Despite dwindling crowds at protest sites, student leaders continue to hold out for their two core demands: full democracy for the former British colony and the resignation of Chief Executive Leung Chun-ying.

They told supporters Tuesday to prepare for a long struggle ahead and threatened fresh civil disobedience if they did not realize their goals, without specifying what actions they might take.

The government in Hong Kong, with Beijing breathing over its shoulder, has already ruled out any progress on either demand.

Instead, it wants to talk about what Lau Kong-wah, undersecretary of the Constitutional and Mainland Affairs Bureau, called “the constitutional basis of the constitutional development” and “the legal requirement of the constitutional development.”

So while talks will take place at 4 p.m. Friday, the agenda remains contested.

Student leaders did not disguise their frustration Tuesday evening, even as they announced the date and time for talks, but appeared to feel that it was better to be seen to be talking than to walk way from negotiations.

“We are very disappointed and angry,” Lester Shum, deputy secretary general of the Hong Kong Federation of Students, told reporters.

He said the government was “not sincere” in its approach to the talks and was resorting to legal arguments instead of facing the central political problem in Hong Kong: a government answerable to Beijing instead of to the citizens of the territory.

“We have a message to the government: Face the people’s demands,” Shum said.

The protesters want a free election for the post of chief executive in 2017, open to candidates nominated by citizens; Beijing intends to vet potential candidates.