Migrants in a caravan of Central American asylum-seekers board buses in Mexicali, Mexico, Thursday, April 26, 2018, for a two-hour drive to Tijuana to join up with about 175 others who already arrived.

A caravan of asylum-seekers from Central America arrived at Mexico's border with the United States on Sunday, numerous reports showed, with supporters on either side of the fence separating Tijuana and San Diego rallying in sight of each other.

Some demonstrators even climbed the border wall that runs right into the Pacific Ocean, sitting and waving as U.S. Border Patrol agents kept careful watch. Dozens of supporters also watched on the American side, where they were held about 20 yards away.

Twitter was awash with posts of the developing situation.

People scale border fence in Tijuana as migrant caravan prepares to seek asylum in U.S. http://on.nbc7.com/eEeaxM

WATCH: Members of migrant caravan gather at U.S.-Mexico border, expected to seek asylum in U.S.

President Donald Trump, who has been calling the caravan a threat to American, has been tracking the progress of the group, which began the journey on March 25 in the Mexican city of Tapachula, near the Guatemala border.

Many of the migrants, said to be fleeing gang violence and poverty in their home countries, are looking to enter the U.S. by seeking asylum. Some of them plan to seek asylum from Mexico.

Disparaging the caravan multiple times during his campaign-style in Washington, Michigan on Saturday evening, Trump called the developments a "mess." He added: "Are you watching this?" He then said, "Our laws are so weak, there's so pathetic, given to us by Democrats, they're so pathetic."

Last week, Trump tweeted about the caravan, while making his case for the tighter border security, and the building of a wall along the U.S.-Mexico border that's he's been promising since the 2016 presidential campaign.

Despite the Democrat inspired laws on Sanctuary Cities and the Border being so bad and one sided, I have instructed the Secretary of Homeland Security not to let these large Caravans of people into our Country. It is a disgrace. We are the only Country in the World so naive! WALL

The Central Americans may provide a test for the Trump administration when they begin seeking asylum at San Diego's San Ysidro border crossing, the nation's busiest. U.S. Customs and Border Protection said the San Ysidro crossing may be unable to take the crush of asylum-seekers all at once, forcing people to wait their turn in Mexico.

Immigration lawyers, who say they want to prepare the migrants for the worst, are warning them they could face possible separation from their children and detention for many months while their petitions for asylum are reviewed.

— The Associated Press contributed to this report.