Trump also tweeted a video Wednesday alleging, without evidence, that Democrats were responsible for allowing a homicidal immigrant into the U.S. The video was reminiscent of the infamous "Willie Horton" ad used against Democratic presidential candidate Michael Dukakis in 1988 and condemned as racist.
But U.S. President Donald Trump ramped up his pre-election focus on the caravan and others behind it, talking of creating a U.S. military force on the border that would outnumber the migrants, many of them women and children.
Asylum claims are initially heard by immigration officers who must determine whether migrants have a "credible fear" of being returned to their home country.
"Seeking asylum is a fundamental human right".
It's not clear how Trump's proposal would work under existing law.
"If they do that with us, they're going to be arrested for a long time", Trump added.
Honduran migrant Jose Macy carries his four-year-old nephew Yair Perez as the thousands-strong caravan of Central Americans migrants hoping to reach the USA border moves onward from Juchitan, Oaxaca state, Mexico, Thursday, Nov. 1, 2018. "They want to throw rocks at our military, our military fights back", he said.
Honduran migrant Saul Guzman, 48, spent the night under a tin roof in the Oaxaca state town of Matias Romero with his son Dannys, 12, before setting out for the town of Donaji, 30 miles (47 kilometers) north.
Asked if he would promise the military will not fire on the migrants, Trump responded with, "I hope they won't, we're going to see".
She said her department had discovered nothing to indicate a "sustained effort to hack voting infrastructure" by any foreign government. "For that reason, we also offered them transportation so that, if possible, tomorrow. they may be able to go to Mexico City or to the place they wish".
FILE - Former Secretary of Homeland Security Tom Ridge speaks to a crowd of hundreds protesting in front of the White House in Washington.
"This complaint is poorly written and looks more like a press release than a lawsuit, using politically charged terms and hyperbole instead of carefully reasoned legal claims", says Breitbart News Senior Legal Editor Ken Klukowski.
TRUMP: "At this very moment, large well-organized caravans of migrants are marching towards our southern border".
Several immigration experts have pointed out the Obama administration did not implement a policy of separating families.
Mr Trump has hardened his stance on migration in a bid to rouse his political base ahead of congressional elections next week.
"Some have been waiting for many years".
The video includes scenes of migrants moving toward the USA and asks ominously, "Who else would Democrats let in?"
US President Donald Trump has deployed thousands of troops to the border as part of his crack down on illegal immigration.
"None of them is a US citizen or a permanant resident", he added, "and none of them is physically in the USA or has ever been physically in the U.S".
In any case, Fox News also reports that there was some confusion over whether the caravan was heading for the California border or for the much closer border crossing in McAllen, Texas.
The parents of six minors, all now travelling north through southern Mexico, are the plaintiffs in a civil action filed Thursday in a District of Columbia court against Trump and nine top Trump administration officials.
Asylum is not a program for those living in poverty.
Trump said there were around 700,000 people inside the country awaiting adjudication of their claims. The United States can not possibly absorb them all.