"We've tried to keep you posted and yet some people, as you just heard in that, felt that this was not a problem," a 'Fox & Friends' co-host said.
Both a current and former DHS official cast doubt on how the department came up with the figure while the caravan is still hundreds of miles away from the U.S. border.
Dozens of demonstrators were alleged to have been killed in clashes with Nigerian security forces in the past week.
"They want to throw rocks at our military, our military fights back. Consider it a rifle," Trump said on Thursday.
"Mexican soldiers hurt, were unable, or unwilling to stop Caravan," Trump tweeted. "Should stop them before they reach our Border, but won't!"
On Monday, Defense Secretary James Mattis and subordinate combatant commanders authorized troops heading to the border to carry live ammunition, according to the documents obtained by Newsweek
The information, contained in operational documents obtained by Newsweek, was transmitted before thousands of troops were directed to the border to meet the migrant caravan.
While El Salvador, Guatemala and Honduras are not undergoing any active conflicts, they have been scarred by wars fueled in part by the U.S.
"What about diseases?" Kilmeade asked. "I mean, there's a reason why you can't bring a kid to school unless he's inoculated."
Republican representatives and pundits have claimed without evidence that Democrats are funding the migrants.
"It's inconceivable that there are not people of Middle Eastern descent in a crowd of more than 7,000 people," the vice president said.
"We seem to have foiled this attempt," a Fox News reporter says of an apparent illegal border crossing.
President Donald Trump also claimed, without evidence, that "unknown Middle Easterners" have joined the immigrant caravan.
"I wish they were carrying heroin. I wish we had thought of it," Barry Bennett, a former Trump campaign adviser, said about the migrant caravan.
More than 14,000 Hondurans have joined the migrant caravan, according to local reports.
Trump said he had alerted the military for what he called a "national emergency."
"Since the day he took office, the Trump administration has implemented policies intended to prevent vulnerable asylum seekers fleeing persecution in their home countries from seeking protection in the U.S.," the Southern Poverty Law Center said.
"The assault on our country at our Southern Border, including the Criminal elements and DRUGS pouring in, is far more important to me, as President, than Trade or the USMCA," Trump tweeted.