China has issued unusually tough warnings for Hong Kong, signalling a desire to bring the semi-autonomous city under tighter control, and “perfect” its governance of the territory, after five months of increasingly violent protests.

China’s Communist party, in a statement issued after a meeting of key leaders, said national interest should take priority over the “two systems” policy that has allowed Hong Kong extensive autonomy since the handover from British colonial rule, and warned that it would not tolerate “any actions that split the country”.

It also called for Hong Kong to perfect its legal system to “safeguard national security”, “strengthen law enforcement power”, and increase “patriotic education” of young people and civil servants, to boost support for China among two vital parts of the population.

The previous day, China’s president, Xi Jinping, had expressed a “high degree of trust” in Hong Kong’s unpopular leader, Carrie Lam, as the two met face to face in Shanghai.

That meeting and the Communist party communique suggest that Beijing is reinforcing its support for Lam – despite speculation she might be replaced – and will keep her in place to preside over attempts to regain control of the city and its streets.

In a clear reference to the five-months of unrest, the statement said officials must prevent “foreign forces” from interfering in Hong Kong or carrying out “subversive activities, infiltration and sabotage”.

Willy Lam, an adjunct professor at Chinese University of Hong Kong, said China was indicating that it would step up control over the city, and its leadership might try to push through a controversial anti-subversion law, shelved after a mass demonstration in 2003, to demonstrate its commitment to Beijing’s goals.

“They are saying that Hong Kong should work harder to push through tough laws,” Lam said. “The current conflicts would not ease but sharpen.”

Xi’s show of support for Lam followed speculation that Beijing was preparing to remove her as city authorities struggle to contain pro-democracy demonstrations that have rocked the financial hub.

Hong Kong’s leader is chosen by a committee with a heavily pro-Beijing makeup, and even Lam has publicly admitted that she struggles to balance the needs of “two masters” – the people of her city and the government in Beijing.

Their meeting in Shanghai on Monday followed another weekend of violence in Hong Kong that was marked by a knife attack and the vandalising of an office of China’s official Xinhua news agency.

Xi said Lam has “done a lot of hard work” and strived to stabilise the situation in Hong Kong, according to a Xinhua report of their meeting.

“Xi voiced the central government’s high degree of trust in Lam and full acknowledgement of the work of her and her governance team,” the state news agency said.

“Ending violence and chaos and restoring order remain the most important task for Hong Kong at present,” Xi said.

Xi also called for “effective efforts” to be made in improving people’s lives and having dialogue with all sectors of society.

Willy Lam said Beijing was showing support for the city’s chief executive “for the time being”.

“It doesn’t mean that they like Carrie Lam, or it doesn’t mean that they think highly of her performance,” he said.

“It’s just that if they don’t seem to be supporting her, then it will be impossible for her to carry out her duty in Hong Kong,” Lam said, adding that Beijing wants Hong Kong to enact national security legislation that would give police more power to punish protesters.

But Carrie Lam could still be sacked within one year or during Beijing’s annual legislative session in March, the expert said.