Donald Trump has said he is prepared to send as many as 15,000 troops to the US-Mexican border to head off a caravan of Central American migrants, a notion described by rights activists as “a racist ploy”.

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The US president floated his latest hardline proposal just two days after announcing the deployment of 5,200 troops to the border and with the midterm elections imminent.

“We’ll do up to anywhere between 10 and 15,000 military personnel on top of border patrol, Ice and everybody else at the border,” the president told reporters at the White House before departing for a campaign rally in Florida. “Nobody’s coming in. We’re not allowing people to come in.”

The caravan is nearly a thousand miles away and would take weeks to reach the US. But Trump claimed: “Oh, they’ll be here fast. They’re trying to get up any way they can. They’re trying to get up by train. They’re trying to get up by truck and by buses. We’re going to be prepared. They’re not coming into our country.”

But the American Civil Liberties Union Border Rights Center condemned the suggestion. Shaw Drake, its policy counsel, said: “Increasing troops for a nonexistent crisis is a racist ploy and an irresponsible waste of resources.”

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A caravan of Central American migrants estimated to number at least 3,500 people left Honduras in mid-October and has advanced 250 miles into Mexico. But it is still nearly 1,000 miles (1,600 kilometers) from the US border.

Currently there are 2,100 national guard troops at the border and the Pentagon said on Monday it was deploying more than 5,200 troops but that the number would rise. On Wednesday, it said more than 7,000 troops drawn from 10 states would support the Department of Homeland Security along the border.

Before Trump’s comments, the defense secretary, Jim Mattis, rejected criticism that deploying thousands of troops to the border with Mexico was a political stunt. “The support that we provide to the secretary for homeland security is practical support based on the request from the commissioner of customs and border police, so we don’t do stunts in this department,” Mattis was quoted as saying by Reuters.

A deployment of 15,000 troops would be roughly equivalent to the size of the US military’s presence in Afghanistan, and three times the size of its presence in Iraq.

The announcement two days ago came as Mexico also cracked down on migrants attempting to cross its own porous southern border.

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Trump, who has long campaigned on the issue of illegal immigration and promised to build a border wall, has declared the caravan a central issue of the midterms. His attempts to whip up fear of the caravan have been reinforced by the conservative Fox News channel. Brian Kilmeade, co-host of Fox & Friends, one of the president’s favourite shows, asked on Monday: “What about diseases?”

The former immigration agent David Ward said on the channel: “We have these individuals coming in from all over the world that have some of the most extreme medical care in the world. And they’re coming in with diseases such as smallpox and leprosy and TB that are going to infect our people in the United States.”

The last known case of smallpox was seen in Somalia in 1977 and the disease was declared eradicated in 1980.

In his exchange with reporters on Wednesday, Trump denied that he was fear-mongering. Asked if the billionaire philanthropist George Soros was funding the caravan, as alleged by baseless conspiracy theories on the right, he said: “I wouldn’t be surprised, I wouldn’t be surprised, … I don’t know who, but I wouldn’t be surprised. A lot of people say yes.”