The INM explained that so far, "the authorities of the Mexican Government have acted in a responsible manner to the requests of Central American migrants, mostly from Honduras, who are asking to enter through the southern border of Mexico.
The organization also urged citizens to quietly enter the nation avoiding any kind of disturbance to public order.
"They were invited to enter the country in an organized and quiet way based on our laws for migrant treatment, which gives priority to vulnerable groups, such as pregnant women, children, the elderly or people with disabilities".
The INM reiterates that in the event of possible acts of violence or the possible irregular entry of some citizens, they will be returned.
"Any person in an irregular situation will be presented to the migration authority, a legal procedure will be initiated and, if necessary, assistance will be provided for the return to their country of origin".
So far, "the authorities of the Mexican Government have acted in a responsible manner to the requests of Central American migrants, mostly from Honduras, who are asking to enter through the southern border of Mexico.
A group of Central American migrants crossed into Mexico on Monday on the Suchiate River, after the closure of the border bridge crossing at Ciudad Hidalgo, Chiapas.
Some fought with the national guards on the river bank, while others slipped through the Mexican officials lines and reached a rural road in small groups. Immigration authorities caught more people there.
Most, however, stayed by the river's edge or stood in its muddy waters after being prevented from crossing the border bridge into Ciudad Hidalgo.
About 5,000 migrants remain on Mexico's southern border with the intention of continuing on to the United States.