Pressed further on his point about whether there was any proof that people from the Middle East were in the caravan, Trump responded, "there very well could be".
Mexican authorities insisted those on the bridge would have to file asylum claims one at a time in order to enter the country.
"We are well aware that this country (Mexico) didn't receive us as we expected, and they can return us to Honduras, and we also know there are drug traffickers who kidnap and kill migrants", Juan Flores, one of those migrants, told AFP.
A senior administration official called the surge a "crisis".
According to numbers released on Tuesday, U.S. border officials arrested almost 397,000 people in total at the southern border in the 2018 fiscal year that ended September 30, a significant increase over the 304,000 apprehended in 2017 but largely in line with arrest trends of migrants at the U.S. southern border over the past decade. The figure he cited was the overall number of known or suspected terrorists stopped from entering the country at all ports of entry. But the new troops would be active duty troops, not National Guard, the US official said.
They are being joined by others from across Central America, creating a group estimated to be about 4,000 strong.
The caravan of migrants moving from Central America to the United States through the Mexican territory now includes around 3,630 people, the Mexican Interior Ministry and Defense Ministry said.
A majority of those walking say they are looking for a better life north of the border are fleeing poverty and violence in Honduras, where the caravan originated.More news: Mourinho rules out loan move for Zlatan Ibrahimovic
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A DHS official declined to answer questions on the tweets.
Tyler Houlton, a spokesman for Homeland Security, later tweeted that the department could confirm that gang members or serious criminals are in the caravan, but he didn't provide details.
In the midst of the campaign for the legislative elections of mid-term, the us president, Donald Trump storm for several days against these migrants, decrying an "assault".
Border arrests dropped in the months after Trump took office in January 2017 but have rebounded over the past year.
"Even if it's a short-term deployment, it's another step toward militarization of our border", Isacson said, adding that 40 percent of people being apprehended at the order are children and families.
The total number of families who arrived at the border during the fiscal year that ended September 30 was 107,212. Apprehensions at the southwest border sometimes exceeded 1 million a year under President George W. Bush.
"The troops retain the right of self-defense, but border patrol officers will still be the ones physically stopping illegal migration", the report noted.
The us president, Donald Trump had said on Monday to have "alerted" the army and the border guard before the arrival of the "caravan" of migrants, an urgent "national" according to him, and threatened to cut off aid paid to countries in central America that have not blocked these migrants.
Under current immigration law, for example, all individuals are entitled to certain rights and legal protections while in the custody of the US government, including illegal aliens.