Hong Kong chief Carrie Lam is expected to hold a press conference on Tuesday afternoon, after protesters rejected a brief statement she put out after a historic march on Sunday as inadequate and impersonal.

However, it was not clear if she would offer further public concessions on the bill at the heart of the crisis. She has already suspended efforts to get it through the city’s legislature, but protesters and opposition figures worry that could leave the government free to return to the law in future.

In a private meeting with a group of about 20 educators on Monday, Lam claimed her decision to suspend the bill on Saturday meant “total withdrawal”, the RTHK news site reported.

Teddy Tang, the chairman of the Association of the Heads of Secondary Schools, quoted Lam telling the closed-doors meeting that her government would not try to pass the legislation again. But it is unclear if she will make a similar commitment in public.

Lam’s announcement on Saturday that she would suspend the bill, days after she promised to ram it through the legislature, was a humiliating climbdown for both Beijing and the woman it had hand-picked to rule Hong Kong.

But it did not satisfy the many people in Hong Kong who are worried that the law would fatally damage the city’s economy and society, by allowing both residents and visitors to be sent for trial in China’s opaque, Communist party-controlled courts.

They came in record numbers on Sunday to march through the city centre, with organisers putting the turnout at nearly 2 million.

The crowd called on Lam to withdraw the law, apologise for police violence, halt a crackdown on activists – and ultimately resign.

Just a few hundred people have turned out at the start of the week as the people of Hong Kong wait for a government response, but there is no question that public anger remains high. Both Lam and Beijing will be weighing the cost of further concessions against the risk of further inflaming tensions.

The Beijing-controlled newspaper Ta Kung Pao said on Tuesday morning that Lam would hold a press conference to apologise again and formally announce the law’s withdrawal, but hours later withdrew the article without providing further detail.

In the meeting with teachers, Lam also apologised for the turmoil of recent weeks, Tang said, but did not appear ready to accept calls for her resignation, saying she wanted to carry on.

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