Donald Trump has threatened to close the whole US-Mexico border, including halting trade with Mexico, if the arrival of migrants from central America there leads to disorder.
He also said he had given troops at the border the go-ahead to use lethal force if needed.
On Monday the US briefly closed a busy crossing to install new barriers.
Thousands of migrants are at the border after travelling more than 4,000km (2,500 miles) from Central America.
They say they are fleeing persecution, poverty and violence in their home countries of Honduras, Guatemala, and El Salvador.
Mr Trump has deployed about 5,800 troops to the border and has previously described the migrants as an “invasion”.
What did Trump say?
“If we find that it gets to a level where we are going to lose control or where people are going to start getting hurt, we will close entry into the country for a period of time until we can get it under control,” he told reporters.
“The whole border. I mean the whole border. Mexico will not be able to sell their cars into the United States where they make so many cars,” he added.