TECUN UMAN, Guatemala (AP) -- A standoff between thousands of Central American migrants trying to reach the United States and Mexican police stretched through the night with some migrants hanging from the closed border gate wailing "there are children here" while others slept on the crowded bridge linking Guatemala to Mexico.
Members of the caravan of more than 3,000 migrants had earlier burst through a Guatemalan border fence and rushed onto the bridge over the Suchiate River, defying Mexican authorities' entreaties for an orderly crossing and U.S. President Donald Trump's threats of retaliation.
But they were met Friday by a wall of police with riot shields on the Mexican side of the bridge. About 50 managed to push their way through before officers unleashed pepper spray and the rest retreated, joining the sea of humanity on the bridge.
Police and immigration agents began letting small groups of 10, 20 or 30 people through the gates if they wanted to apply for refugee status. Once they file a claim, they can go to a shelter to spend the night.
As night fell on the bridge, the migrants' frustration turned to despair as women clutching small children took up the rows in front of the gate pleading with the Mexican federal police. Some migrants yelled "We are hungry!" Others wailed that they had children while others set up tarps to prepare for the night sleeping on the increasingly dirty and befouled bridge.
"Please, it is night. Let us pass," Alba Luz Giron Ramirez, a former shop employee and mother of three, pleaded to the officers.
Giron said they had come from San Pedro Sula, Honduras, and that gangs had killed her brother and threatened her.
"We want them to give us permission to go to Mexico," her 5-year-old son Ramon said in a child's voice. "We wouldn't stay."
Alison Danisa wept as she knelt in the garbage already piling up on the bridge, clutching her naked 11-month-old infant to her breast.
"We have suffered so much. She has a fever and we brought nothing," she said, showing the baby's bare bottom to indicate they had no diapers.
A Mexican marine official with a loudspeaker approached the gate and told migrants they would be taken in trucks to "a humanitarian attention center" in Tapachula, a border city in the Mexican state of Chiapas. But the official did not say when this would happen.
Late Friday night, Mexican President Enrique Pena Nieto said in an address to the nation that a large group of migrants had "tried to enter Mexican territory irregularly, attacking and even hurting some elements of the Federal Police."
"Mexico does not permit and will not permit entry into its territory in an irregular fashion, much less in a violent fashion," he said.
Honduran President Juan Orlando Hernandez tweeted late Friday that he spoke with his Guatemalan counterpart, Jimmy Morales, and asked permission to send Honduran civil protection personnel to the bridge to help the migrants.
"I also asked authorization to hire ground transportation for anyone who wants to return and an air bridge for special cases of women, children, the elderly and the sick," Hernandez tweeted.
Hernandez and Morales are expected to meet in Guatemala early Saturday to discuss the situation.
Some migrants, tired of waiting, jumped off the bridge into the Suchiate River on Friday. Migrants organized a rope brigade to ford its muddy waters, and some floated across on rafts operated by local residents who usually charge a dollar or two to make the crossing.
Acner Adolfo Rodriguez, 30, one of the last migrants through the breached Guatemala border fence, said he hoped to find work and a better life far from the widespread poverty and gang violence in Honduras, one of the world's deadliest countries.
"May Trump's heart be touched so he lets us through," Rodriguez said.
The U.S. president has made it clear to Mexico that he is monitoring its response. On Thursday he threatened to close the U.S. border if Mexico didn't stop the caravan. Later that day he tweeted a video of Mexican federal police deploying at the Guatemalan border and wrote: "Thank you Mexico, we look forward to working with you!"
Mexican officials said those with passports and valid visas -- only a tiny minority of those trying to cross -- would be let in immediately.
Migrants who want to apply for refuge in Mexico were welcome to do so, they said, but any who decide to cross illegally and are caught will be detained and deported.
U.S. Secretary of State Mike Pompeo met Friday with President Enrique Pena Nieto and Foreign Relations Secretary Luis Videgaray in Mexico City, with the caravan high on the agenda.
At a news conference with Videgaray, Pompeo called illegal migration a "crisis" and emphasized "the importance of stopping this flow before it reaches the U.S. border," while also acknowledging Mexico's right to handle the crisis in a sovereign fashion.
"Mexico will make its decision," Pompeo said. "Its leaders and its people will decide the best way to achieve what I believe are our shared objectives."
At Mexico City's airport before leaving, Pompeo said four Mexican federal police officers had been injured in the border standoff and expressed his sympathy.
On Thursday, Videgaray asked the U.N. for help processing what Mexico expects to be a large number of asylum requests.
Migrants have banded together to travel en masse regularly in recent years, but this caravan was unusual for its huge size, said Victor Clark Alfaro, a Latin American studies professor at San Diego State University. By comparison, a caravan in April that also attracted Trump's ire numbered about 1,000.
"It grabs one's attention that the number of people in these kinds of caravans is on the rise," Clark Alfaro said. "It is migration of a different dimension."
Elizabeth Oglesby, a professor at the University of Arizona's Center for Latin American Studies, said people join caravans like this because it's a way to make the journey in a relatively safe manner and avoid having to pay thousands of dollars to smugglers. She disputed Pompeo's assertion that that there is a "crisis" of migration.
"The border is not in crisis. This is not a migration crisis. ... Yes, we are seeing some spikes in Central Americans crossing the border, but overall migration is at a 40-year low," Oglesby said.
Speaking on the Televisa network, Videgaray did not seem concerned about Trump's threat to close the U.S.-Mexico border, saying it had to be viewed in light of the hotly contested U.S. midterm elections, in which Trump has made border security a major campaign issue.
Videgaray noted that 1 million people transit the border legally every day, and about $1 million in commerce crosses every minute.
"Before taking decisions of that kind," Videgaray said, "there would be many people in the United States ... who would consider the consequences."
Associated Press writers Peter Orsi, Christopher Sherman and Maria Verza in Mexico City contributed to this report.