On the eve of what could be the biggest turnout yet in Hong Kong’s continuing protests, and a crucial test of wills on both sides, a demonstration that began with physical confrontation between authorities and pro-democracy demonstrators shifted Tuesday into a public relations duel aimed at the mass of undecided residents here.

Three days into protests that have brought large parts of the city to a standstill, both sides appeared to be carefully plotting their next move. Some pro-democracy leaders demanded a meeting with Hong Kong’s chief executive and threatened new acts of civil disobedience if the demand is not met.

The actors in Wednesday’s drama will be the protesters and authorities of Hong Kong, but the mainland Chinese leadership will be following events closely. Huge public protest is anathema to Beijing, and what happens in Hong Kong over the next day or two could shape the Chinese response.

The demonstrators have called for a large showing on the first day of a big two-day holiday and say they’re not backing down.

In his first media briefing since police lobbed tear gas Sunday night into largely peaceful crowds, Hong Kong Chief Executive Leung Chun-ying gave no indication that he would be willing to meet with organizers but acknowledged the protests were likely to continue for a long time.

Hong Kong’s political fault line with Beijing

“They have set up a lot of resource centers and even first-aid points,” he pointed out in a televised statement. “So we know that [the protest] . . . is not a matter of days, but it will last for a relatively long time.”

Organizers hope the protests will grow significantly in size and momentum as Hong Kong takes two days off for the holiday Wednesday and Thursday, making it possible for hundreds of thousands of workers to join. If big crowds do not turn up, the momentum of the demonstrations could be sapped.

In his statements, Leung tried to appeal to Hong Kong residents’ practical side, painting the protests as not just a nuisance, but also an out-of-control movement that is hurting Hong Kong’s image and its economy.

“Its impact on the people’s daily lives, their personal safety in the event of emergencies, the city’s economic development, as well as the cost on its international image, will also grow bigger and bigger,” he said.

Meanwhile, demonstrators tried to make inroads of their own with smaller gestures, not just picking up their trash from the night before but sorting it for recycling, distributing umbrellas to fend off brief showers and passing out donated food and water among themselves.

By protesting, activists are trying to force Beijing’s Communist Party leaders to abandon newly declared powers to weed out any candidates in the upcoming Hong Kong election for Leung’s successor. And the cordial nature of the protests over the past three days has perhaps been their most distinctive quality.

In putting a strong emphasis on the “civil” part of their civil disobedience, protesters are trying to sway large portions of the public that until recently have remained on the fence about an occupation of Hong Kong’s all-important financial district.

Authorities in Hong Kong cracked down on pro-democracy demonstrators on Sunday using tear gas and pepper spray. Thousands of demonstrators turned out on the downtown streets again on Monday to support the protest. (The Washington Post)

But the protesters’ behavior is also an expression of modern Hong Kong society’s quirks, in which citizens are obsessed with efficiency, often finicky about following regulations and take seriously social responsibility and courtesies.

That mix over the past few days has yielded surprising and at times incongruous images of politely raucous demonstrations.

At points where their occupation has diverted traffic, some protesters posted signs pleading for understanding and explaining why they were demonstrating. Volunteers positioned themselves with makeshift ladders to help people cross uneven areas of the protest site. Nursing students wore homemade red crosses taped to their sleeves as they ran first-aid stations. Some students could be seen doing homework while sitting in the streets.

In sweltering heat Tuesday, some protesters began walking through the crowds with spray bottles offering refreshing mists of water.

Leung has tried to appeal as well to Hong Kong’s polite, practical side in urging protesters to go home. “We don’t want Hong Kong to be messy,” he said Monday.

And some in Hong Kong remain unswayed by protesters’ efforts. Small arguments broke out Tuesday as small-business owners and others opposed to the protests angrily confronted demonstrators downtown.

In one of several videos posted online, a businessman jeered student protesters, telling them to go back to school.

Both sides are trying so hard to woo the middle because Hong Kong is home to a substantial silent majority — residents who do not wish to engage or pick sides in Hong Kong’s fight with Beijing and are largely focused on their jobs, businesses and other more immediate concerns.

“Most people in Hong Kong are not political animals, and most people also realize Beijing will not change its mind” in tightening its grip over Hong Kong’s politics and government, said Willy Lam, an analyst at the Chinese University of Hong Kong. “That’s what makes these protests so surprising and spontaneous.”

But despite the numbers, Beijing has traditionally been loath to give in to such public pressure. President Xi Jinping has spent considerable political capital consolidating his power and fostered some resentment among party officials by cracking down on corruption. Giving in to democratic demands in Hong Kong could make him look vulnerable, some experts say.

And as Xi’s subordinate in Hong Kong, Leung has limited options to defuse the situation. In his statement Tuesday, Leung did not lay out any plan for quelling the protests and refused to say whether his officials would meet with demonstrators.

Beijing, Leung argued, will not bend. “The Chinese government won’t give in to threats asserted through illegal activity,” he said Tuesday.

As a result, he may not be able to do anything to appease protesters and can only wait for their momentum to run out.

“That’s why,” said Michael Davis, a law professor at the University of Hong Kong, “the end game right now is winning hearts and minds of Hong Kong people. Both sides need the public on their side to win.”

Liu Liu and Gu Jinglu in Beijing contributed to this report.