Members of a Central American migrant caravan that drew the wrath of President Donald Trump during its month-long journey through Mexico to the U.S. border scaled the border fence and rallied in support of migrant rights on Sunday.

U.S. border authorities said Saturday that some people associated with the caravan had already been caught trying to slip through the fence and encouraged the rest to hand themselves in to authorities.

READ MORE: Migrants in caravan in Mexico ignore warnings of stern U.S. response

The group of about 400 migrants from Honduras, Guatemala and El Salvador arrived in border city Tijuana on buses over the past couple of days, and most of them said Saturday they intended to legally seek asylum in San Diego on Sunday.

Later on Sunday, some migrants will go to the border and attempt to request U.S. asylum. U.S. authorities have advised that there may be delays in their ability to process the migrants and that some “may need to wait in Mexico as [border officials] work to process those already within our facilities.”

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WATCH: Family fleeing poverty, violence in Mexico’s migrant caravan seek American dream

1:08 Family fleeing poverty, violence in Mexico’s migrant caravan seek American dream Family fleeing poverty, violence in Mexico’s migrant caravan seek American dream

Lawyers advising the group warned the migrants on Saturday that not everyone will be successful. Asylum seekers must demonstrate a well-founded fear of persecution at home and the overwhelming majority of those from Central America are denied refuge in the United States. Those denied asylum are generally deported to their home countries.

READ MORE: What are these ‘caravans’ of migrants that Donald Trump is concerned about?

Migrants without strong asylum cases were advised to remain in Mexico, although the Mexican government has not said whether it will allow them to stay.