President Donald Trump - in full midterms push - claimed on on Monday that "Criminals and unknown Middle Easterners are mixed in" with the caravan of Central American immigrants making its way to the U.S. -Mexico border.
The number of migrants swelled to about 5,000 as more people continue to join the group that stretches for about a mile.
She added in a subsequent tweet that she has been in "constant contact" with her foreign counterparts in Mexico, Guatemala and Honduras, and that her department was monitoring the situation and ready to provide assistance if necessary.
About a thousand migrants, including women and children, were still stranded on a border bridge hoping to enter Mexico legally via Guatemala. "If they fail to do that, the USA will turn them away", he said.
They received help at every turn from sympathetic Mexicans who offered food, water and clothing.
Maria Teresa Orellana, a resident of the neighborhood of Lorenzo handed out free sandals to the migrants as they passed.
One of the migrants marching to Ciudad Hidalgo, Luis Miguel Martinez, 30, also said his goal was to find work in the United States so he could feed his family, including two daughters he left behind in Honduras.
Mexico's federal government said on October 20 that almost "900 migrants" arrived in the country via unauthorized means. The advances have overwhelmed Mexican officials' attempts to stop them at the border. But "they are going to continue walking, and their feet won't heel as long as they keep walking", he said.
Group of thousands of migrants from Central America on journey to US ahead of midterm elections.
The Red Cross said Saturday that numerous people it is helping along the caravan route, a majority of them women and children, "are suffering from dehydration, stomach infections, and foot injuries as they walk the long journey".
The group's decision capped a day in which Mexican authorities again refused mass entry to migrants on the bridge, instead accepting small groups for asylum processing and giving out 45-day visitor permits to some of them.
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In front of a crowd of about 700, including Mayor Bill de Blasio, billionaire Michael Bloomberg, and Gov. Haley has often been an unpredictable and independent force in the Trump administration.
Throngs of people continued to wait on the bridge border crossing, where on Saturday morning many pressed for limited opportunities to plead their case to immigration officials, while many others opted to cross the river illegally, either on jury-rigged rafts or by swimming.
Approximately 640 migrants requested asylum in Mexico, according to a statement from the Mexican government and the National Migration Institute. Authorities handed out numbers for people to be processed in a strategy seen before at USA border posts when dealing with large numbers of migrants. They were not detained on reaching the Mexican bank.
Numerous migrants, the overwhelming majority fleeing violence and poverty in Honduras, slept on the bridge through heavy rain overnight, dozens of them crammed against a metal border gate guarded by Mexican police.
I have alerted Border Patrol and Military that this is a National Emergy.
"When I heard about the caravan, I knew it was my chance", he told the newspaper, noting his cousin and uncle still live in California and that he called them to let him know he was coming.
Thousands of would-be migrants are stranded on the border between Guatemala and Mexico, after Mexican police blocked their bid to reach the US.
Mexico's ambassador to Guatemala Luis Manuel Lopez told AFP the women and children would be processed by immigration authorities and taken to a shelter in the city of Tapachula, 40 kilometers (25 miles) away.
He said the migrants' rights must be protected as they break into Mexico and head north.
Passing freight trucks were quickly boarded by dozens of migrants, and straining tuk-tuks carried as many as a half-dozen.
Yesterday, the United States Secretary of State, Mike Pompeo issued a statement informing that the U.S. is concerned about the migrant caravan and their unsafe journey through Guatemala and Mexico.
Mr. Hernandez said about 500 migrants were in transit back to Honduras, a roughly 12-hour trip by road.
Later in the day, authorities in Guatemala said another group of about 1,000 migrants had entered that country from Honduras.