While lawyers disputed that such unilateral action by the president could eliminate a right guaranteed by the US constitution, some agents reassured potential clients that the policy would at least remain unchanged for a couple of years. Others reported growing interest in services in Canada, which also grants birthright citizenship.

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Mifubaby, a Beijing-based agent offering services for pre- and post-maternity services in Los Angeles and Saipan, said it was not easy to amend the US constitution so there was little need to worry now.

“As the world’s most developed country based on the rule of law, it would take at least two or three years to get this done, even though it’s the president’s idea,” an agency staff member said.

Staff at several other Shanghai-based maternity agencies also said they doubted the plan would be realised and their services would remain unchanged.

Global Baby-Mom and Baby Care Centre, an agent operating in Canada, said it had received more inquiries since Trump’s comments were published on Tuesday.

“It was like an earthquake … We got a lot of requests for advice and many who planned to go to the US are considering Canada. It’s still totally fine to give birth in Canada and the baby can get Canadian citizenship,” the company said on its microblog account.

There are no official statistics on how many Chinese women give birth in the US, but Mifubaby estimated that the number had risen from just 600 in 2007 to more than 80,000 in 2016.

Industry sources say that interest in the services has grown amid food safety scandals, pollution and growing competition for limited public resources in China.

Having a baby in the US and spending the first month there after delivery, known as yuezi, or absolute rest, according to Chinese tradition, can cost Chinese families hundreds of thousands of yuan.

Sources said Chinese women usually concealed their pregnancy on entering the US with a visitor visa and stayed in maternity centres, often in Los Angeles or Saipan, where they are cared for by Chinese nannies until the baby is a month old.

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Some Chinese internet users welcomed Trump’s announcement, saying that it was unrealistic to pin hopes for the future on another country.

“Stop thinking about how to escape our motherland. It’s a good thing to focus on how to improve our own country,” one commenter wrote on Weibo, China’s version of Twitter.

Prominent US senator Lindsey Graham, a South Carolina Republican, has described birthright citizenship as “absurd”.

“This policy is a magnet for illegal immigration, out of the mainstream of the developed world, and needs to come to an end,” he said.

Under the 14th Amendment to the US constitution, citizenship is granted to “all persons born or naturalised in the United States”.

But Graham contended that the US Supreme Court had never ruled on the issue of whether birthright citizenship applied to children born of illegal immigrants in the United States.

Still, lawyers doubted that Trump could use an executive order to end the constitutional right.

Hao Junbo, a Beijing-based lawyer experienced in cross-border litigation and US law, said that even if Trump issued the executive order, it could be rejected for violating the US constitution.

“It would definitely lead to litigation. So the legal result is very unpredictable,” Hao said.

“I think the main purpose is to appeal to voters by cracking down on immigrants, to win support for the coming election.”