A group of about 150 migrants carrying white flags that read, "La paz y Dios," or "Peace and God are With Us," separated from the larger caravan near Southern California and inched within 500 feet of the U.S., a report Thursday said.

The migrants said they are carrying the white flags to show that they are peaceful, and will attempt to present themselves as asylum seekers near Baja, Calif., The San Diego Union-Tribune reported.

President Trump on Thursday threatened to close the border with Mexico if his administration determines that Mexico has lost control of the situation. The Union-Tribune reported that Mexican federal police held a barrier near a pedestrian crossing and urged the migrants to apply for jobs in Tijuana. Police claimed there are thousands of jobs in the city. Federal police were dressed in riot gear and prevented the caravan from getting closer to the U.S.

Carlos Lopez, a Honduran who was leading the small group, told the paper that the conditions in Mexico are horrible. He said there are sick children and women and children are forced to remain outside in the elements. Those already in the city have camped out in tents, slept on dirt fields or under bleachers or are staying in overcrowded shelters throughout the city as they wait to figure out their next steps.

"The whole world is watching what is happening here," he said.

The report said the larger group contains about 6,219 Central Americans. The federal government estimates the number of migrants could grow to 10,000 in the coming weeks, or months. President Trump warned that the caravan is a national security threat and it will not enter the U.S.

On Monday, a judge barred the president from enforcing a ban on asylum for those who cross the U.S. border illegally – a decision the administration said would cause “countless illegal aliens to pour into our country."

The report said that the migrants who traveled for over a month can now see a bridge that separates them from the U.S.

Speaking to reporters while in Florida for the holiday, Trump threatened to close the U.S. border with Mexico for an undisclosed period of time if his administration determines that its southern ally has lost "control" on its side.

Trump also said he has given the thousands of active-duty troops he sent to the border before the Nov. 6 midterm elections the "OK" to use lethal force against migrants "if they have to." And he said Homeland Security Secretary Kirstjen Nielsen, whom he has faulted for not being tough enough on immigration, is "in there trying."

Fox News' Andrew O'Reilly contributed to this report