A 19-year-old Hong Kong activist facing secession charges under the city's national security law was detained Tuesday amid reports he planned to attempt to claim asylum at the United States consulate.

Police said two men and one woman -- aged between 17 and 21 -- were arrested Tuesday in relation to allegedly secessionist comments on social media.

Studentlocalism, a onetime pro-independence group, identified the three on Facebook as its former convenor Tony Chung, and former members William Chan and Yanni Ho.

According to a little known United Kingdom-based activist organization, Friends of Hong Kong, which said it had been working with Chung, he had been planning to claim asylum at the US consulate to Hong Kong prior to his arrest.

All three Studentlocalism members were previously arrested in July in connection with posts made on social media by a page claiming to represent the international arm of the group.

The Hong Kong branch of the organization said it had disbanded soon after the national security law was imposed on the city by Chinese authorities, banning secession, subversion and collusion with foreign forces.

Police accused Chung and others still based in Hong Kong of continuing to advocate for the city's independence from China, a crime that carries with it a sentence of three to 10 years, or up to life imprisonment for offenses of a "grave nature."

The accused denied having any connection to the allegedly secessionist posts in question.

A Hong Kong government spokesman told CNN on Wednesday that it would not comment on media reports of the arrests but said there would be "no justification for any so-called 'political asylum' for people in Hong Kong.""It should be stressed that people in Hong Kong are prosecuted for acts in contravention with the laws of Hong Kong, regardless of their political beliefs or backgrounds.

Moreover, trials are conducted by an independent judiciary in accordance with the principle of the rule of law," he added.A growing number of Hong Kongers have successfully applied for asylum overseas since the national security law was passed earlier this year.

Washington has said it will prioritize refugees from Hong Kong, and US politicians have been among the most vocal in criticizing China's ongoing crackdown on the city's autonomy and democratic freedoms.

Providing refuge to activists within Hong Kong itself would be a major escalation however, and could cause a diplomatic firestorm for both Washington and Beijing, potentially imperiling the future of the Hong Kong consulate itself.

CNN has reached out to the US Consulate General in Hong Kong and the Hong Kong and Macau Affairs Office for comment. According to US law, Washington "does not grant asylum in its diplomatic premises abroad."

Those seeking to claim refugee status must be present in the US to do so. While in the past some activists have been granted protection by the US embassy in Beijing, this has been exceptionally rare, and each time caused major political headaches for Washington.

In 1989, following the crackdown on Tiananmen Square, dissident academic Fang Lizhi fled to the US embassy, where he spent over a year before Beijing agreed to allow him to leave China.

In 2012, legal activist Chen Guangcheng, after months under house arrest, made a dramatic break for the embassy during a visit to Beijing by then Secretary of State Hillary Clinton. He too was eventually permitted to leave the country, after tense negotiations between US and Chinese officials.

When disgraced former Police Chief Wang Lijun sought refuge at the US consulate in Chengdu that same year, however, he was turned away. Wang was eventually sentenced to 15 years in prison on corruption charges.

The difference between an embassy and a consulate may be key. Embassies are protected under international law, and to close one or enter the premises would spark a major diplomatic crisis.

Consulates, however, are less protected, and countries can order for them to stop operations, as the US and China both did earlier this year with tit-for-tat closures of each country's respective missions in Houston and Chengdu.

During that incident, which came after Washington claimed China's Houston consulate was implicated in espionage operations, US officials also accused Beijing's mission in San Francisco of harboring a fugitive Chinese scientist.

That scientist, Tang Juan, later surrendered to police in California.The circumstances around Tang's surrender remain unclear, but it may have been prompted by fears the US could have moved to close the San Francisco consulate if she had continued to shelter inside.

Similar concerns could make US officials shy away from granting any refuge to dissidents in Hong Kong, the most important US mission in greater China after the Beijing embassy.

During the consulate stand off earlier this year, some Chinese state media publications called for the Hong Kong consulate to be closed, accusing the US of running influence operations out of it.

While Beijing appears to have shied away from any greater escalation for now, losing the Hong Kong mission would be a major blow for Washington, both diplomatically and practically, given the economic importance of Hong Kong and the number of Americans who live in the city.