Current Foreign Relations Secretary Luis Videgaray was also sanguine and viewed things through the lens of USA politics.
In Mexico City, US Secretary of State Mike Pompeo said after meeting his Mexican counterpart that migration across the two countries' border is reaching "a moment of crisis".
Police deployed pepper spray after some migrants tried to push their way through the Mexican side.
United States President Donald Trump is threatening to deploy the military and close the country's southern border as more Hondurans and Salvadorans join thousands of migrants in Guatemala heading north. Several busloads of Mexican federal police unloaded from buses with their riot gear at the border crossing in Ciudad Hidalgo. About 50 managed to push their way through before officers unleashed pepper spray and the rest retreated.
In a series of raging tweets, the United States president urged Mexico to "stop this onslaught" and prevent the would-be immigrants from entering the US. Others were carrying young children in their arms.
The caravan has been growing steadily since it left the violent Honduran city of San Pedro Sula on Saturday. One migrant said: 'One way or another, we will pass'.
"Only God on high can stop us", Escobar told the AP.
Earlier Friday, Mexico's ambassador to Guatemala said his country meant to enforce what he called a policy of orderly entry in the face of the thousands trying to cross.
Gerard Butler explains why he canceled Saudi Arabia trip amid Khashoggi's disappearance
Permission apparently came after a late Sunday-night call between King Salman and the Turkish president, Recep Tayyip Erdoğan. Secretary of State Mike Pompeo is meeting now with Saudi King Salman over the disappearance of Saudi writer Jamal Khashoggi.
"If these people are really concerned about persecution, fear and death and they want to claim political asylum, they are now out of Honduras".
"There is nothing there", Orellana said.
And the president-elect, Andrés Manuel López Obrador, has pledged to issue work visas for Central Americans in a bid to retain workers in the area rather than seeing them moving to the US.
Any who decide to cross illegally and are caught will be detained and deported, the Mexican government has said.
Trump has told Mexico that he is monitoring the country's response.
It was the second time in six months that Trump suggested the possibility of military action to curb immigration at the U.S. -Mexico border.
The people seen in this video - virtually all of whom were women, female children, and women with small children - apparently each received a single banknote as they walked down a line, but the largest banknote in Guatemala is worth 200 Quetzales (approximately $25).
White House officials say if an individual evades the new system and reaches the USA border, Mexico will now allow the refugees to be returned to its country.
He also informed migrants of the serious risks posed by "irregular entry" into the country, including migrant smuggling and human trafficking networks.
In his series of Thursday tweets, Trump threatened to rip up a recently signed trade agreement with Mexico if Enrique Peña Nieto's government doesn't act to stop illegal immigration and the drug trade at the border, with Mexican drug cartels making an estimated $19-29 billion per year on drug sales in the US.