The nonpartisan Pew Research Center estimates there were about 11.3 million immigrants in the USA illegally in 2016, the most recent data available.
Trump has also told the US military mobilizing at the southwest border that if USA troops face rock-throwing migrants, they should react as though the rocks were rifles. Immigration officials have turned away asylum-seekers at border crossings because of overcrowding, telling them to return at a later date.
He claimed the caravan of migrants is causing " a crisis on our southern border" and added: "This is a perilous situation (that will) become even more hazardous". So far, it is not certain whether any operative suffered any injury but Guatemalan officers were hurt.
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In a series of TV interviews Mr Trump said, without citing evidence, that the caravans of migrants travelling through Central America were "a lot larger than it's reported", adding they were "no angels". "We're going to consider it, I told them, consider it a rifle". There are billions of people in the world living at the poverty level.More news: India Thrash Windies by Nine Wickets, Clinch Series 3-1
Her responses, while more articulate than the president's, perpetuated the administration's fear-mongering narrative about immigration and specifically targeted the caravan heading to the border from Honduras that has become a political pawn ahead of the midterm elections.
The caravan of migrants is still hundreds of miles from the border.
That's because asylum-seekers, along with unaccompanied children from countries other than Mexico and Canada, have special protections enshrined in law, based on the principle that vulnerable individuals should have a chance to have their claims heard before they are shipped back to potential danger.
But the government has been flummoxed by what Kevin McAleenan, commissioner of Customs and Border Protection, calls the "asylum gap": the inability to stop people from making false claims for asylum and living legally in the US for years while their cases proceed.
Earlier in the day, a third caravan of migrants - this time from El Salvador - waded over the Suchiate River into Mexico on Friday, bringing another 1,000 to 1,500 people who want to reach the USA border.More news: USA charges financier, former Goldman bankers for 1MDB
The offer of buses to Mexico City and the subsequent reversal came after the migrants' request for buses to the capital were ignored by the Mexican government days earlier when they were in Juchitan, Oaxaca state. "We are going to make it or die trying", he said.
Trump has already ordered over 5,000 troops to secure the border from the approaching caravans. The second group includes Hondurans, Salvadorans and some Guatemalans.
"This case is not ripe for adjudication, but regardless, if President Trump issues a presidential proclamation denying entry to this class of aliens, then Supreme Court precedent makes clear Congress has given him the legal authority to do so", he said.
The Pentagon says more than 7,000 active-duty troops are being sent to the Southwest border, with more possible.
The speech follows a series of proposals and statements on immigration that Trump's opponents have called outlandish stunts.More news: Curry sets National Basketball Association records as Warriors thump Nets