TAPANATEPEC, Mexico — Coordinators of a caravan of several thousand Central American migrants moving through southern Mexico urged its members to rest Sunday. At first the migrants vowed to press on anyway but later changed their minds amid reports that a child had been abducted.

The migrants said they would stay and hold a meeting Sunday in Tapanatepec. Late Saturday night, groups of migrants were running through the town's streets saying a migrant's child had been snatched. Something similar led to a panic at an earlier stop, but was not confirmed.

After being delayed for a couple hours when federal police halted their exit from the town of Arriaga Saturday morning, most of the migrants arrived in Tapanatepec in the searing heat. Dozens headed down to the Novillero river below the central square to bathe, wash clothing and cool off. Others lined up at a medical aid station mostly for attention to their battered feet.

For the first time an arm of the federal government seemed to be directly helping the migrants advance rather than trying to diminish the caravan. In this case Grupo Beta, Mexico's migrant protection agency, gave rides to stragglers and passed out water.

At the caravan's regular evening meeting in the town square, its coordinators tried to force a little chivalry.

Many of the migrants have depended on hitchhiking to move between towns rather than walking the entire way. When trucks stop, it's usually young men who sprint to reach them first. Women carrying children or pushing strollers are at a disadvantage.

On Saturday night, a nun scolded the men and urged the women to be more aggressive in pursuing the rides. She said the church would help arrange five trucks to transport only women with children on the next trek to Niltepec about 33 miles away.

"To me it's bad because there has to be equality because we are all struggling on this path," said Hector Alvarado. The 25-year-old from Atlantida, Honduras said he had to quit school and leave his wife and 2-year-old daughter to try to make a living in the U.S.

Rosa Bonilla is traveling with a 10-year-old daughter and a son who will turn 2 this year. The single mother conceded that she never beat the men to the trucks that stopped, but said some men looked out for the mothers and made sure they got on.

"I don't agree that it should only be women with children," she said. She argued that husbands should be allowed on because they help protect the women.

"If we go alone anything could happen," she said.

The Mexican government seems torn between stopping the migrants from traveling toward the U.S. border or burnishing its international human rights image.

On Saturday, more than a hundred federal police dressed in riot gear blocked a rural highway in southern Mexico shortly before dawn to encourage the migrants to apply for refugee status in Mexico rather than continuing the long, arduous journey north. U.S. President Donald Trump has urged Mexico to prevent the caravan from reaching the border.

Police let the caravan proceed after representatives from Mexico's National Human Rights Commission convinced them that a rural stretch of highway without shade, toilets or water was no place for migrants to entertain an offer of asylum. Many members of the caravan have been travelling for more than two weeks, since a group first formed in San Pedro Sula, Honduras.

Not long after the caravan resumed its advance Saturday, government officials lent them a hand.

Martin Rojas, an agent from Mexico's migrant protection agency Grupo Beta, said he and his fellow agents planned to use agency pickup trucks to help stragglers catch up with the caravan.

"There are people fainting, there are wounded," said Rojas, who spoke to The Associated Press after dropping off a group of women and children in Tapanatepec, where the caravan planned to spend the night. Rojas transported the group to their destination after spotting them on a highway trudging through temperatures approaching 104 degrees Fahrenheit.

The caravan still must travel 1,000 miles to reach the nearest U.S. border crossing at McAllen, Texas. The trip could be twice as long if the 4,000 or so migrants head for the Tijuana-San Diego frontier, as another caravan did earlier this year. Only about 200 in that group made it to the border.

Most of the migrants in the caravan appeared determined to reach the U.S., despite an offer of refuge in Mexico.

Mexican President Enrique Pena Nieto launched a program on Friday dubbed "You are home," which promises shelter, medical attention, schooling and jobs to Central Americans who agree to stay in the southern Mexico states of Chiapas or Oaxaca, far from the U.S. border.

Mexico's Interior Ministry said that temporary identity numbers have been issued to 111 migrants under the program. The IDs, called CURPs, authorize the migrants to stay and work in Mexico, and the ministry said pregnant women, children and the elderly were among those who had joined the program and were now being attended at shelters.