SANTA ROSA DE COPAN, Honduras — Hundreds of Hondurans traveling in vehicles and on foot converged on the Guatemalan border on Tuesday, part of a new migrant caravan bound for the United States which President Trump has already used as fresh ammunition in his fight for border wall funding.The caravan began departing from the northern Honduran city of San Pedro Sula on Monday night. Others set off throughout the day on Tuesday. Honduran authorities estimated that between 800 and 1,000 people were in the caravan, while officials from Honduras’ National Human Rights Commission put the range between 1,500 and 2,000.Mr. Trump, whose dispute with Congress over his demand for $5.7 billion for a border wall between Mexico and the United States has led to a partial shutdown of the federal government since Dec. 22, warned on Twitter on Tuesday about the new mass migration.“A big new Caravan is heading up to our Southern Border from Honduras,” he wrote. “Only a Wall, or Steel Barrier, will keep our Country safe! Stop playing political games and end the Shutdown!”The Trump administration has excoriated Central American and Mexican governments for failing to stop the caravans, which met little resistance at the various international borders they crossed on the way north.In a show of muscle on Tuesday, however, the Honduran government vowed vigilance at its border with Guatemala and said it had detained 60 minors without proper travel documents to leave Honduras.“The border and the illegal crossings are reinforced,” Julián Pacheco, the Honduran security minister, told reporters on Tuesday. “If people are going to leave, they have to leave through legal, authorized points.”The Mexican government has also vowed to harden its southern border to block the passage of any undocumented migrants in the latest caravan. Olga Sánchez, the country’s interior minister, said that officials had identified about 370 illegal points of entry along its border with Guatemala and planned to monitor them to prevent illegal crossings.Tens of thousands of Hondurans and other Central Americans have migrated north in recent years, fleeing rampant violence and poverty. Some have chosen to move in large, semi-coordinated groups or caravans, offering participants a degree of security against the many perils that lurk on the migrant trail, including muggings, extortion and rape.Until last year, most caravans went largely unnoticed. But a migration that began in southern Mexico last spring drew the attention of Mr. Trump, who warned that the group posed a threat to the United States’ sovereignty.An even larger group set off from Honduras in October, drawing the ire of Mr. Trump as well as international media attention. It was followed by other groups and by mid-November, more than 6,000 migrants, nearly all from Central America, had made it as far as Tijuana.Hundreds of them have applied for asylum in the United States while others have tried to cross the border illegally. Still others have decided to remain in Mexico, availing themselves of the Mexican government’s offer of humanitarian visas and work permits. Hundreds more, frustrated with their inability to cross legally into the United States, have been voluntarily repatriated to their homes in Central America.But neither the dashed hopes of so many from last year’s caravans nor Mr. Trump’s threats seemed to discourage many of the participants in the latest caravan.“Even though a wall is being built, that’s not going to stop us,” said Junior Aleman, 17, who was walking with a group of about a dozen migrants through the mountains of western Honduras on Tuesday. The group had left San Pedro Sula on Monday night and, through a combination of walking and hitching rides, were making their way toward the Honduras-Guatemala border crossing at Agua Caliente.He intended to try to cross illegally into the United States and head for Virginia, where two of his aunts lived. There, he said, he planned to find a job — something that had been hard to come by in Honduras.“There’s no work and I want to help my family,” he said.