Hong Kong's embattled leader warned the United States on Tuesday not to "interfere" with her government's response to the city's pro-democracy movement, after fresh protests called on Washington to ramp up pressure on Beijing.

Millions of people have demonstrated over the last 14 weeks in the biggest challenge to China's rule of the financial hub since its handover from Britain in 1997.

Protesters took to the streets again on Sunday, marching to the American consulate to call on Congress to pass a bill expressing support for the pro-democracy movement.

The proposed law could undermine Hong Kong's special US trade privileges by mandating regular checks on whether authorities were respecting the Basic Law that underpins the city's semi-autonomous status.

But Hong Kong's pro-Beijing Chief Executive Carrie Lam said that any change to its economic relationship with Washington would threaten "mutual benefits".

"It's extremely inappropriate for any country to interfere in Hong Kong's affairs," she told reporters.

"I hope that no more people in Hong Kong actively reach out to tell the United States to pass the act." While some American politicians on both sides of the aisle have expressed support for the democratic goals of the protesters, President Donald Trump's administration has maintained a more hands-off approach while it fights a trade war with China.

Trump has called for a peaceful resolution to the political crisis and urged Beijing to not escalate with a violent crackdown.

But he has also said it is up to China to handle the protests.

Washington has rejected Beijing's allegations that it is backing the demonstrators and China has provided little evidence to back its claims beyond supportive statements from some US politicians.

Separately, more than 150 lawmakers in Britain have called on Foreign Secretary Dominic Raab to offer second citizenship and the right of abode to residents of Hong Kong.

That would "send a strong message to China that the people of Hong Kong are not alone", the open letter said.

Hong Kong's protests were lit by a plan to allow extraditions to the authoritarian mainland, seen by opponents as the latest move by China to chip away at the city's unique freedoms.

After Beijing and city leaders took a hard line, the movement snowballed into a broader campaign calling for greater democracy, police accountability and an amnesty for those arrested.

The protests show no signs of abating, and Lam has struck an uncompromising tone for much of the last three months.