(Releads with Hong Kong leader's tactic)
* Protesters demand Hong Kong leader steps down
* Chief executive seen prepared to sit it out for weeks
* National Day celebrations pass peacefully
* Tens of thousands still out on the streets
* Rights groups say some mainland activists detained
By Donny Kwok and James Pomfret
HONG KONG, Oct 1 (Reuters) - Hong Kong authorities will not immediately move to clear tens of thousands of pro-democracy protesters occupying large areas of the city, and will let them stay for weeks if need be, a source with ties to leader Leung Chun-ying said on Wednesday.
In contrast, students spearheading the protest movement ratcheted up pressure on Leung, saying they would occupy more government buildings unless the Beijing-backed chief executive stepped down by Thursday night.
Hong Kong protesters are angry about China's decision to limit voters' choices in a 2017 leadership election, and, in a major challenge to Beijing's authority in Hong Kong and beyond, have brought much of the financial hub to a standstill.
As the mass action approached its sixth day on Wednesday evening, the number of people on the streets remained high.
Fears among demonstrators that police might try to remove them forcibly ahead of the National Day holiday marking the establishment of the People's Republic of China in 1949 proved unfounded, and the atmosphere was calm but defiant.
Hong Kong student leader Lester Shum issued an ultimatum to Leung: step down or else face wider protests.
"We will escalate the action if CY Leung doesn't resign by tonight or tomorrow night. We will occupy more government facilities and offices," he told protesters.
"I believe the government is trying to buy more time. They want to use tactics such as sending some people to create chaos so that they would have a good reason to disperse the crowd."
Riot police had used tear gas, pepper spray and baton charges at the weekend to try to quell the unrest, but tensions have eased since then as both sides appeared ready to wait it out, at least for now.
Protesters have dug in, setting up supply stations with water bottles, fruit, disposable raincoats, towels, goggles, face masks and tents.
Leung has said Beijing would not back down and that Hong Kong police would be able to maintain security without help from People's Liberation Army troops from the mainland.
According to a government source with ties to Leung, the chief executive appeared ready to allow the anger to subside, and would only intervene if there was looting or violence.
"Unless there's some chaotic situation, we won't send in riot police ... We hope this doesn't happen," the source said. "We have to deal with it peacefully, even if it lasts weeks or months."
Leung could not be immediately reached for comment.
The protests are the worst in Hong Kong since China resumed its rule of the former British colony in 1997.
They also pose one of the biggest political challenges for Beijing since it violently crushed pro-democracy protests in Tiananmen Square in 1989.
China has dismissed the protests as illegal, but in a worrying sign for the Communist Party leadership in Beijing, the demonstrations have spread to neighbouring Macau and Taiwan.
On Wednesday, hundreds of people moved into Hong Kong's Tsim Sha Tsui, a shopping area popular with mainland Chinese visitors. It would normally be doing roaring trade during the annual National Day holiday.
The celebrations went ahead peacefully, although scores of students near the ceremony at Bauhinia Square booed as the national anthem was played.
A beaming Leung shook hands with supporters waving the Chinese flag, even as protesters who want him to stand down chanted: "We want real democracy."
"We hope that all sectors of the community will work with the government in a peaceful, lawful, rational and pragmatic manner ... and make a big step forward in our constitutional development," Leung said in a speech.
The Hong Kong and Chinese flags billowed in the wind at the completion of the ceremony, but one of the main protest groups said they marked the occasion "with a heavy heart".
Cracking down too hard on the movement could shake confidence in market-driven Hong Kong, which has a separate legal system from the rest of China. Not reacting firmly enough, however, could embolden dissidents on the mainland.
China rules Hong Kong under a "one country, two systems" formula that accords it some autonomy and freedoms not enjoyed in mainland China, with universal suffrage an eventual goal.
However, protesters reacted angrily when Beijing decreed on Aug. 31 that it would vet candidates wishing to run for Hong Kong's leadership.
In contrast to National Day celebrations in Hong Kong, hundreds of people attended a tightly choreographed flag-raising ceremony in Tiananmen Square in Beijing. The daily event was typically austere, with goose stepping troops and a brass band.
Communist Party leaders in Beijing worry that calls for democracy could spread to the mainland, and have been aggressively censoring news and social media comments about the Hong Kong demonstrations.
A strongly worded editorial in the People's Daily, the Communist Party mouthpiece, attacked the "Occupy Central" protests as being confrontational.
"And now, a handful of people are bent on confronting the law and stirring up trouble. (They) will eventually suffer the consequences of their actions," it said on Wednesday.
Rights groups said that a number of mainland activists supporting the Hong Kong protests had been detained or intimidated by police on the mainland.
The turmoil has hit the share market, with the city's benchmark index falling 7.3 percent over the past month. Markets are closed on Wednesday and Thursday for the holiday.
Some banks and other financial firms have begun moving staff to back-up premises on the outskirts of the city to prevent growing unrest from disrupting trading and other critical functions, two business services firms said.
Mainland Chinese visiting Hong Kong had differing views on the demonstrations.
"For the first time in my life, I feel close to politics," said a 29-year-old tourist from Beijing surnamed Yu. "I believe something like this will happen in China one day."
But a woman surnamed Lin, from the southern Chinese city of Shenzhen, said the protesters' demands for a democratic election were "disrespectful to the mainland".
In Taipei's Liberty Square, some 5,000 mostly young protesters, many wearing symbolic yellow ribbons in a show of solidarity, encouraged Hong Kong people to fight for democracy.
The Hong Kong protests have been watched closely in Taiwan, which has full democracy but is considered by Beijing as a renegade province that must one day be reunited with the mainland.
Taiwan President Ma Ying-jeou has said Beijing needed "to listen carefully to the demands of the Hong Kong people".
In the former Portuguese colony of Macau, which like Hong Kong is now a Chinese "special administrative region", organisers said around 1,200 people gathered in a show of solidarity at Friendship Square.
Former Hong Kong governor Chris Patten called for genuine consultation over demands for greater democracy.
"I think we've got to see dialogue replacing tear gas and pepper sprays," Patten, the last British governor before the 1997 handover of the territory to China, told BBC radio. (Additional reporting by Irene Jay Liu, Farah Master, Diana Chan, Twinnie Siu, Yimou Lee, Kinling Lo, Charlie Zhu, John Ruwitch, Clare Baldwin, Diana Chan and Anne Marie Roantree in HONG KONGSui-Lee Wee in BEIJING, Michael Gold and J.R. Wu in TAIPEI and Stephen Addison in LONDON; Writing by Paul Tait, Jeremy Laurence and Mike Collett-White; Editing by Mike Collett-White)