President Donald Trump has issued an executive order for an “impassable physical barrier” to be built along the US border with Mexico.
He also signed an action to strip funds from US cities that are sanctuaries for undocumented immigrants.
Mr Trump said in a TV interview with ABC News that Mexico would “absolutely, 100%” reimburse the US for his wall.
But Congress would have to approve funding for the structure, which is estimated to cost billions of dollars.
Building a 2,000-mile barrier along the Mexican border was one of Mr Trump’s key pledges in the election campaign.
What did Trump say?
He spoke of a “crisis” on the southern US border as he signed the directives during a ceremony at the Department of Homeland Security on Wednesday.
The orders also called for hiring 10,000 immigration officials to help boost border patrol efforts.
“A nation without borders is not a nation,” he said. “Beginning today the United States gets back control of its borders.”
How will President Trump deliver on border wall promise?
Mr Trump said relations with Mexico – whose President Enrique Pena Nieto he is scheduled to meet at the end of the month – would get “better”.
A ban on some Muslim-majority countries
The executive orders are among a flurry expected on national and border security this week.
Mr Trump is next expected to announce immigration restrictions from seven African and Middle Eastern countries.
An eight-page document that appears to be a draft executive order has been obtained by various US media and the BBC.
It suggests Mr Trump will suspend the Syrian refugee programme indefinitely and the wider refugee programme for four months.
The president also plans to suspend issuing visas from unnamed countries deemed to pose a threat to the security of the US.
Immigration lawyers have told the BBC they believe those countries are Syria, Iraq, Iran, Libya, Sudan, Somalia and Yemen.
But the White House has refused to comment on the document, and it may be revised before being signed.
Mr Trump backed off an early campaign pledge to ban all Muslims from entering the US.
What are sanctuary cities?
The term applies to cities in the US that have policies in place to limit the assistance given to federal immigration authorities.
It got traction in the 1980s after Los Angeles told its police force to stop questioning people solely to determine their immigration status in 1979.
And in 1989, San Francisco passed an order that prohibited the use of city funds to enforce federal immigration laws.
Now there are hundreds of these areas – they are not always cities – and they include San Diego, Los Angeles, Seattle, Denver, Austin and Boston
Trump’s order to block federal grants could cost these cities millions of dollars. But the administration may face legal challenges, given that some federal courts have backed cities that say they cannot hold immigrants beyond their jail term at the say-so of federal authorities.
On Wednesday, Mr Trump was joined by parents whose children, he said, had been “horribly killed by individuals living here illegally”.
He read out their names and invited the parents to stand.
“For years the media has largely ignored the stories of Americans and lawful residents victimised by open borders,” he added.
‘Mexico is going to pay for wall’
Earlier on Wednesday, Mr Trump told ABC News he would recoup costs of the wall from Mexico.
“There will be a payment. It will be in a form, perhaps a complicated form,” he said.
Mr Trump has previously estimated the wall would cost $8bn (£6.4bn), but critics have said it could be nearly double that sum.
Earlier on Wednesday, Mr Trump also promised a “major investigation into voter fraud”.
He tweeted that the inquiry would focus on those registered to vote in two states and dead registered voters.
This week he claimed that between three and five million illegal immigrants had voted for Hillary Clinton, but offered no evidence.
Mexicans see wall as racist – Will Grant, BBC News, Mexico City
Mexicans might disagree about a lot – especially on the political and economic direction of the country.
But if there is one thing around which almost all of Mexico can coalesce, it is their profound opposition to the US border wall.
From the Mexican side of the border, it is seen as a policy which is intended to break up families and prevent ordinary people from looking for seasonal work in the north – the kinds of jobs, they note, which prop up the US economy.
Others go further, and consider the entire border wall to be a racist and xenophobic policy.
Either way, Mexicans from the president’s office to the factory floor agree that the country will not pay for a wall they don’t want and didn’t call for.
They say they won’t finance the project either at the time of building or in the future.
That’s not to say some Mexicans aren’t in favour of changes to immigration.
Many are aware of the risks that their countrymen take by crossing illegally into the US, especially through dangerous border regions such as the Arizona desert.
Rather than a wall with their neighbour to the north though, they want to see comprehensive immigration reform including guest worker programmes and temporary work visas.
The view from the border – James Cook, BBC News, San Diego
President Trump’s Great Wall faces formidable legal, diplomatic and logistical obstacles.
Even some border patrol agents say privately that they are not sure that the project is possible.
They do, however, welcome planned increases in resources and staffing.
But here in San Diego on the southern border of the United States, there is much fear in the shadows.
President Trump’s action on immigration is bold, sweeping – and intensely divisive.