Washington - President Donald Trump on Wednesday ordered work to begin on building a wall across the Mexican border, angering his southern neighbour with his hardline stance on immigration.The US leader instructed officials to begin to "plan, design and construct a physical wall along the southern border" and - perhaps more problematically - see how it could be funded."A nation without borders is not a nation," Trump said, echoing former president Ronald Reagan, as he visited the Department of Homeland Security to sign two executive orders."Beginning today, the United States of America gets back control of its borders," the Republican president said.Hours later, Mexican President Enrique Pena Nieto demanded "respect" for his country in a nationally televised address."I regret and condemn the decision of the United States to continue construction of a wall that, for years, has divided us instead of uniting us," Pena Nieto said."I have said it time and again: Mexico will not pay for any wall," Pena Nieto said.MeetingA Mexican government official told AFP that Pena Nieto will weigh in the coming days whether to maintain a meeting with Trump in Washington on Tuesday.Stemming immigration was a central plank of Trump's election campaign.His signature policy prescription was to build a wall across the 3 200km border between the United States and Mexico.Some of the border is already fenced, but Trump says a wall is needed to stop illegal immigrants entering from Latin America.The policy has become a clarion call for the US right and far-right - the core of Trump's support.A Morning Consult/Politico poll released on Wednesday said 47% of voters support building a wall, with 45% against.Experts have voiced doubts about whether a wall would actually slow illegal immigration, or if it is worth the billions it is expected to cost."I suspect that a lot of Trump supporters would be just as happy with a big statue of a middle finger pointed south," said Congressman Luis Gutierrez."Both are about equally effective as national security strategies."Billion-dollar wallDespite the high-octane rhetoric, Trump's action was piecemeal, looking to identify existing funds that could be diverted toward the project.The Republican-controlled Congress would need to supply billions of dollars more if the wall is to be anywhere near completed.Trump's party has spent the last decade preaching fiscal prudence, so cuts to existing programs would likely be required.Trump also ordered a survey of the border to be completed within 180 days.Much of the land needed to build the wall would have to be seized from private citizens in Texas, the state of Texas or tribal authorities.That could lead to lengthy legal proceedings, political blowback and substantial expropriation payments."The only real solution to reform our immigration system is to pass comprehensive immigration reform that provides a path to citizenship for the 11 million" undocumented people in the United States, top Senate Democrat Chuck Schumer said.Make Mexico pay?Trump has promised to make Mexico pay for the wall, something the Mexican government has repeatedly said it will not do."Ultimately it will come out of what's happening with Mexico, we're going to be starting those negotiations relatively soon. And we will be, in a form, reimbursed by Mexico," Trump told ABC earlier on Wednesday.Trump aides have weighed hiking border tariffs or border transit costs as one way to "make Mexico pay." Another threat is to finance the wall by tapping into remittances that Mexican migrants send home, which last year amounted to $25 billion."There are a lot of different ways of getting Mexico to contribute to doing this, and there are different ways of defining how exactly they pay for it," House leader Paul Ryan said in an interview on MSNBC, while also conceding that the United States is "going to pay for it and front the money up."Mexican Foreign Minister Luis Videgaray and the country's economy minister are currently in Washington to prepare for Pena Nieto's visit next week, which now hangs in the balance.Economy Minister Ildefonso Guajardo warned that Mexico could walk away from the negotiations if the US governments threatens remittances or insists on the wall payment.Ban on Muslims?Trump is also said to be floating the idea of a ban on refugees from Muslim-majority countries, including Syria.Around 4.8 million Syrians have fled to neighboring countries alone, according to the United Nations. An estimated 18 000 Syrians have come to the United States.Former officials said Trump could slow the flow down by moving resources away from processing visa requests, or cutting or freezing migrant quotas and programs.The move has prompted a fierce backlash even before it was announced."A ban on refugees would not make America safer," said Stephen Yale-Loehr of Cornell Law. "Refugees from Syria already go through a 21-step screening process that takes 18-24 months.""The head of the US Citizenship and Immigration Services told Congress in September 2016 that not a single act of actual terrorist violence has been committed by a refugee since 9/11."