SUCHIATE RIVER • Mexican security forces fired tear gas at rock-hurling Central American migrants who waded across a river into Mexico, in a scramble that saw mothers separated from their children.

Monday's clashes between hundreds of US-bound Central Americans and the Mexican National Guard underscores the challenge President Andres Manuel Lopez Obrador faces to contain migration at the bidding of his US counterpart Donald Trump.

The mostly Honduran migrants numbered around 500, Mexico's National Migration Institute (INM) said. They were part of a group of several thousand people that had left Honduras last week, fleeing rampant gang violence and dire job prospects in their homeland.

Video footage showed groups of migrants throwing rocks at a few members of the National Guard militarised police who were on the banks of the river trying to thwart illegal crossings, while hundreds of others ran past into Mexico.

Five National Guard police were injured in the clashes, the INM said.

"We didn't come to stay here. We just want to cross to the other side," said Ingrid, 18, from Honduras. "I don't want to go back to my country because there is nothing there."

A Reuters witness spoke to at least two mothers whose young children went missing amid the chaos, as the migrants on Mexican soil scattered to try and avoid being detained by officials.

The INM said it had detained 402 migrants and transferred them to immigration stations where they will get food, water and shelter. The INM will send them back home via plane or bus if their legal status cannot be resolved.

A spokesman at the INM said the institute had no reports of children going missing amid the clashes.

The Reuters witness said that several kilometres from the border, the Mexican immigration authorities had filled a bus and pickup trucks with detained migrants.

Honduras' ambassador to Mexico Alden Rivera said the Mexican authorities have some 1,300 Hondurans in migration centres and would start sending them back home by plane and bus yesterday.

Mr Trump has threatened to punish Mexico and Central American countries economically if they fail to curb migrant flows, resulting in a series of agreements aimed at making good on his campaign promises to curb immigration at the United States' border with Mexico.

Over the weekend, at least 2,000 migrants were at the Guatemalan border town of Tecun Uman, opposite Ciudad Hidalgo on the Mexican side. They appeared to grow impatient on the bridge over the Suchiate River that connects the two countries, after some were denied permission to cross by assembled Mexican migration officials.

The INM said it informed the migrants it could not allow them to cross into Mexican territory to "transit" through and blamed the group's organisers for "ignoring the risk to minors and at-risk people" by crossing the river.

Mexico has offered migrants work in the south, but those who do not accept it or seek asylum will not be issued safe conduct passes to the US, and most will be deported, the Interior Ministry said. It said on Sunday that Mexico had already received nearly 1,100 migrants in the states of Chiapas and Tabasco.

Guatemala said at least 4,000 people have entered from Honduras since last Wednesday, in one of the biggest surges since three Central American governments signed accords with the Trump administration obliging them to assume more of the responsibility for dealing with migrants.

REUTERS