Amnesty International also called on Latin American governments to let people enter and apply for protections.
Representatives for the White House and the US Border Patrol did not immediately reply to requests for comment.
Lorenzana added that El Salvador has significantly reduced violence, a key driver of migration, and that the flow of Salvadoran migrants has dropped 60 per cent in two years.
US President Donald Trump has said he has alerted the Border Patrol and military that the caravan of people heading to the US/Mexico border is a national emergency.
A team of AP journalists traveling with the caravan for more than a week has spoken with Hondurans, Guatemalans and Salvadorans, but has not met any Middle Easterners, who Mr Trump suggested were "mixed in" with the Central American migrants.
There are now 2,100 National Guard performing support jobs that help to free up Department of Homeland Security personnel to patrol the border, Davis said.
The Central American countries receive more than $500 million in federal aid from the USA every year.
The migrant caravan, which started out more than a week ago with less than 200 participants, has drawn additional people along the way.
The Republicans now have control of both chambers of Congress.
Mr. Trump has been complaining about that situation for months. But "they are going to continue walking, and their feet won't heal as long as they keep walking", he said. In California, where farmers usually rely on workers from Mexico to bring in the harvest, many Mexicans are staying away, preferring to find work in their own country.
"IOM reports that large numbers of people are arriving in Mexico today and are likely to remain in the country for an extended period", United Nations deputy spokesman Farhan Haq said, urging that they be treated with "respect and dignity". He said all those there were from Central America.
This is not the first caravan to threaten the southern border.
At the time of this tweet, the migrant caravan numbered roughly 1,600.
Even though the goal is to reach the USA border, she said: "We only want to work and if a job turns up in Mexico, I would do it".
"Fortunately, Congress - not the President - has the power of the purse, and my colleagues and I will not stand idly by as this administration ignores congressional intent", Representative Eliot Engel of NY, the top-ranking Democrat on the House Foreign Affairs Committee, said in a statement emailed to reporters.
Guatemala received $177 million of US aid in fiscal-year 2016, according to USAID. That money funds programs that promote economic development and education, as well as supporting democracy and human rights, among other issues.
The president previously vowed to send the USA military, as opposed to the National Guard, to confront the group, which the United Nations now estimates is over 7,200 members strong. "The courts are asking the U.S.to do things that are not doable!"
But Mr. Trump said he's also not thrilled with Mexico's response.
Despite Mexican efforts to stop them at the Guatemala-Mexico border, about 5,000 Central American migrants resumed their advance toward the USA border Sunday in southern Mexico.
The United Nations High Commissioner for Refugees (UNHCR) is now on the ground in Mexico assisting authorities in ensuring that migrants have access to the country's asylum system.
The "migrant caravan" marched north into Mexico from Guatemala over the weekend; setting the stage for a major showdown with the Trump administration when they reach the USA border sometime this week.
Trump tweeted last Tuesday that he had "strongly informed" Honduran President Juan Orlando Hernandez that he would eliminate aid to his country if he didn't stop the massive caravan bound for the U.S.
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