The request for bus travel for all also indicates an increased sense of urgency amongst the caravan's members to make it to the USA border - despite thousands of American troops awaiting them there and a steady drumbeat of warnings from President Trump and US officials to turn around.
Trump has been escalating his already aggressive attacks on undocumented immigrants ahead of the November 6 midterm elections.
Customs and Border Patrol Commissioner Kevin McAleenan said Tuesday that USA authorities are tracking the caravan of refugees, now estimated at around 3,500 people, as well as another group between Guatemala and Mexico of about 3,000 people.
The president said he would issue a comprehensive executive order about these new policies in a week. "And so when the president and supporters of his or people around him attack George Soros and say Soros is funding this caravan, they are trafficking in a well-known and historic anti-Semitic trope". Trump did not say if he obtained the alleged information from USA intelligence agencies, Mexican intelligence officials or right-leaning cable news outlets.
It is not clear whether the plan would pass legal muster.
In a lengthy speech Thursday, Trump said migrants are abusing the asylum system and making a "mockery" of immigration laws.
"We don't do stunts", Mattis said Wednesday. "We have a lot of everything".
"We're not going to put up with that".
Under US immigration law, any immigrant in the US can apply for asylum regardless of how he or she entered the country.
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Democratic Senate Minority Leader Chuck Schumer and Democratic House Minority Leader Nancy Pelosi also opted not to participate. Tree of Life Rabbi Jeffrey Myers told ABC on Monday that the President of the United States was always welcome to visit.
Immigrant rights groups are expected to challenge any limits placed on access to asylum.
He lied that his administration is building his promised border wall, he lied about asylum-seekers, he stoked conspiracy theories about the Central American immigrant caravan, and he lied about the number of undocumented immigrants in the country.
A first caravan, which has dwindled and now numbers some 4,000 people, according to an aid group called Pueblos sin Fronteras, arrived Tuesday in the town of Juchitan, in Oaxaca, while a smaller group of 2,000 people managed to cross the Suchiate River separating Mexico from Guatemala the day before.
Mexican officials and forces "Should stop them before they reach our Border, but won't!"
"We will consider that a firearm", Trump told reporters on November 1, Fox News reported. We're not allowing people to come in'. But many migrants are unaware of that guidance, and official border crossings have grown increasingly clogged.
The Department of Defense says the number of troops deployed could change at any time, potentially on a daily basis.
"Our military is being mobilised at the Southern Border", Trump tweeted. "Some have been waiting for many years".
Trump also said the USA is building "massive" tent cities to house asylum seekers, including children, while their claims are processed. But in recent days, officials from Mexico's immigrant-protection agency have organized rides for straggling women and children on the caravan as a humanitarian effort.