San Diego (CNN) At least 158 Central Americans who traveled in a migrant caravan through Mexico have crossed into the United States this week to seek asylum, organizers said Thursday.

Pueblo Sin Fronteras, or People Without Borders, which organized and guided the journey, said 70 people from the caravan were among those who crossed Thursday into the San Ysidro, California, port of entry near San Diego. The migrants will make their case for why they should be granted asylum.

The group estimates 70 migrants remain at camps and shelters on the Mexican side of the border. They are expected to cross the border and seek asylum.

The migrants say they're fleeing violence and poverty in Central America and hope they'll find safety and security in the United States.

President Donald Trump has tweeted that these migrants shouldn't be allowed into the country . Vice President Mike Pence called the caravan "a deliberate attempt to undermine the laws of this country and the sovereignty of the United States."

Our Southern Border is under siege. Congress must act now to change our weak and ineffective immigration laws. Must build a Wall. Mexico, which has a massive crime problem, is doing little to help! — Donald J. Trump (@realDonaldTrump) May 4, 2018

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