From behind his desk in the Oval Office, President Donald Trump signed a flurry of executive orders and decrees aimed at cracking down on immigration.

From one order tackling the definition of birthright citizenship, to another declaring illegal immigration at the border a national emergency, Trump swiftly made moves on his promises to tighten the US-Mexico border.

But some of his plans - particularly around changing the definition of birthright citizenship - are likely to face significant hurdles.

He is already facing legal challenges from immigration advocacy groups, which have reacted furiously to his announcements.

One organisation said his plans "do not uphold American values", and another said Trump's administration was "actively trying to destroy our lives".

In his inaugural address earlier in the day, Trump vowed that "all illegal entry will be halted" and that millions of "criminal aliens" would be deported.

He also signed an order declaring Mexican drug cartels terrorist organisations. "I have no higher responsibility than to defend our country from threats and invasions," he explained.

At another event at Washington's Capital One Arena, Trump formally revoked nearly 80 executive actions of his predecessor Joe Biden. He had previously vowed to scrap Biden's policies "within five minutes".

Following his inauguration, he also signed a proclamation that gave officials the authority to "repel, repatriate, or remove" migrants until he was satisfied that "the invasion at the southern border has ceased".

Although the details of the order are not yet known, officials have said that Trump plans to end birthright citizenship.

That refers to an approach of the US government whereby anyone born on American soil is considered a citizen at birth, regardless of their parents' immigration status.

Trump appears to be seeking to change the rules so that that the children of undocumented migrants living in the US will no longer automatically be considered US citizens. It would not apply retrospectively.

Exactly how he intends to achieve this is unclear, however, because birthright citizenship is enshrined in the constitution and would require a two-thirds vote in both chambers of Congress to change.

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Trump has instructed federal agencies to stop issuing documentation to children born in the US to parents who are in the country illegally or on temporary visas, which could effectively deny them access to public services.

Advocacy group the American Civil Liberties Union (ALCU) immediately said it was suing the Trump administration over the order. "Denying citizenship to US-born children is not only unconstitutional - it's also a reckless and ruthless repudiation of American values," it said in a statement.

The new administration has also moved to swiftly scrap CBP One, a mobile application used by migrants to book appointments to appear at a port of entry.

Biden administration officials had credited the app with helping reduce the number of detentions at the border since it was first introduced in January 2023. It was the only legal pathway to request asylum at the US-Mexico border.

Now, the Customs and Border Protection website notes that the app is "no longer available".

App users also now are shown a message noting that "existing appointments scheduled through CBP One are no longer valid".

According to CBS, the BBC's US partner, the Biden administration had scheduled roughly 30,000 appointments via CBP One for migrants to enter the US in the next three weeks.

Other estimates had suggested that as many as 270,000 migrants were in Mexico waiting for an opportunity to enter the US using CBP One.

In the Mexican border city of Tijuana, some migrants reported feeling defeated and deflated after learning of CBP One's demise.

"I hope God touches his [Trump's] heart," said Oralia, a Mexican woman who fled cartel violence in her home state along with her epileptic son. "We really do need the help."

She had been waiting for an appointment through CBP One for seven months.

Among his other day-one moves, Trump ordered a shutdown of another Biden-era initiative, which allowed up to 30,000 migrants from Cuba, Haiti, Nicaragua and Venezuela to fly to the US per month. Like the CBP One app, it was designed to lower the numbr of illegal crossings.

Immigration advocacy groups have reacted furiously to Trump's various orders.

As well as the criticism from the ACLU, the president and CEO of the National Immigration Forum said the orders were "disappointing but not surprising".

"The expected orders would separate families and weaken our economy," Jennie Murray's statement continued. "They do not uphold American values."

Greisa Martinez Rosas, the executive director of United We Dream - a national immigrant youth organisation - said that the orders show that the administration "will spend the next four years actively trying to destroy our lives".

"Trump's pledges to carry out mass raids and deportations will have devastating consequences on communities nationwide, leaving millions of families and individuals in disarray if immediate action is not taken by our elected officials to publicly fight back," she added.

(With additional reporting from Will Grant in Mexico)