MEXICO CITY — President Trump’s State of the Union speech hit hard on a topic that has dominated his term in office: defending the border with Mexico against what he described as migrants in “large organized caravans.”

He also suggested that the Mexican authorities were encouraging the migrants to cross the border illegally.

“We have just heard that Mexican cities, in order to remove the illegal immigrants from their communities, are getting trucks and buses to bring them up to our country in areas where there is little border protection,” Mr. Trump said in his speech Tuesday night.

Some aspects of Mr. Trump’s assertions are true but others are unsubstantiated or distorted. There is no evidence, for example, that the Mexican authorities are sending migrants to weak points along the border.