President Trump said Thursday that the thousands of migrants heading for the southern U.S.-Mexico border are not "legitimate asylum seekers."

"The government of Mexico has generously offered asylum, jobs, education and medical care for people within the caravan, but many members of the caravan have refused these offers, which demonstrate that these migrants are not legitimate asylum seekers," Trump said at the White House on Thursday. "They are not looking for protection because if they were, they would be able to get it from Mexico."

An estimated 1,600 migrants are heading to the U.S. to seek asylum. The group started in early October with an initial 160 Hondurans, but hundreds more have joined the caravan.

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Trump said Wednesday that he is sending up to 15,000 troops to the border before the first caravan arrives. The president said the troops are necessary to ensure that the U.S. is "not letting them in."

"The United States cannot possibly absorb them all. Asylum is a very special protection for those fleeing government persecution based on race, religion, and other protected status," Trump said, before adding that the Democrats are "largely responsible" for encouraging these migrants through their laws and judges.

"These caravans and illegal migrants are drawn to our country by Democrat-backed laws and left wing judicial rules. We are getting rules that are so ridiculous, so bad, they are writing the laws. Can't do that," Trump said.