Changes to detention rules saw thousands of migrant children detained and separated from their parents earlier this year, sparking national and worldwide condemnation.
Some 4,000 migrants fled their lives of poverty and violence in the Central American country with the hope of making it to the United States - despite repeated warnings from President Trump that he would deploy the U.S. military to stop them.
The remark came during Thursday's broadcast of The Five, where Kennedy, known primarily for her self-titled program on the network, sat as a panelist for a discussion on immigrants during which she argued the government hasn't implemented sufficient border control. And what will happen if they do?
Could Trump successfully stop all US tax-funded foreign aid to these nations?
The Guatemalan government branded the caravan "illegal".
An estimated 10% of the population of Guatemala, El Salvador and Honduras have fled danger, forced gang recruitment and dismal economic opportunities.
Launched Saturday from Honduras, the caravan reportedly has grown to more than 4,000 people, including whole families and - in some cases - children traveling without their parents.
Donald Trump was elected after promising to get tough on immigration and build a wall along the border with Mexico.
Any who decide to cross illegally and are caught will be detained and deported, the Mexican government has said.
In 2016, it was estimated that 400,000 migrants pass through Mexico every year.
Most migrants are carrying few belongings, taking what they can carry in backpacks, as they head out on the almost 2,800 mile (4,500km) trek.
The migrants have agreed that they will begin their journey to the border crossing between Guatemala and Mexico around 11 a.m. local time. Those who do so will be held "at a migratory station" for up to 45 business days.
Migrants with proper papers or who wish to apply for asylum will be allowed to enter Mexico, the ministries added.
Central Americans have free passage within their region, but crossing into Mexico they are required to present a visa.
The Mexican ambassador to the US made the claim that they had reason to believe the migrant caravan from Honduras heading to the USA border was politically motivated. Before dawn Friday, the migrants chose to wait a few more hours for stragglers to arrive.
Beyond that, this situation catches Mexico at a unusual time.
"It's a situation that is nearly impossible to resolve at this time for Mexico", Salazar told CNN en Español Thursday.
In response to their deployment, Trump tweeted, "Thank you Mexico", on Thursday, just hours after threatening to deploy the USA military and "close our southern border" - potentially upending a recent trade deal with Mexico and Canada.
In April, Trump said that he wanted to deploy more USA troops on the border until the completion of his planned wall between the United States and Mexico.
When asked if Mexico will take Trump's threats to withhold aid seriously, Gutierrez said a conversation with the USA is important, but stressed the complexity of the situation.
In addition to this latest caravan now at the Mexico-Guatemala border, a US border patrol official tells CBS News there has been an increase in large groups attempting to cross into the USA together.
The group chanted: 'We are not smugglers, we are migrants, ' as they reorganized themselves on Friday afternoon.
In a statement, the country's Institute of Migration (IGM) said: "Guatemala does not promote or endorse irregular migration in any forms, and therefore rejects movements organized for unlawful purposes which distort human rights, like migration, for their own end".
It's also about Mexican emigrants living overseas, many of whom are undocumented.
Central American migrants hiked from Honduras through muddy jungle and residential streets, some toting babies along with backpacks, Reuters images show.
Mexican President Enrique Peña Nieto has partnered with the United States in the past on immigration-related issues.
Lopez Obrador wants to avoid repression against migrants and also to avoid angering the United States. So that makes any global policy negotiations tricky. He said this week that Mexico would offer jobs to Central Americans.
"Can you believe this, and what Democrats are allowing to be done to our Country?" he said. "We are not going to attend to the issue only with deportations or means of force".
Marcelo Ebrard, Mexico's foreign minister-designate, downplayed Trump's comments as aimed at his domestic political base.
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