US President Donald Trump has threatened to close the whole US-Mexico border, including halting trade with Mexico, if the arrival of migrants from central America leads to disorder.
He also said on Thursday that he had given troops at the border the go-ahead to use lethal force if needed, BBC reported.
On Monday, the US briefly closed a busy crossing to install new barriers.
Thousands of migrants are at the border after travelling more than 4,000 km from Central America.
They say they are fleeing persecution, poverty and violence in their home countries of Honduras, Guatemala, and El Salvador.
Trump has deployed about 5,800 troops to the border and has previously described the migrants as an "invasion".
"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 US where they make so many cars," he added.
Trump's reference to lethal force came after Defence Secretary James Mattis said military police at the border would be unarmed.
"They don't have guns in their hands, there is no armed element going in," he told reporters on Wednesday.
On Thursday, Trump also warned that the US government could shut down next month if no more money was provided for a wall between the US and Mexico.
"Could there be a shutdown? There certainly could and it will be about border security, of which the wall is a part," he said.
He has renewed his attacks after earlier saying a federal judge who blocked his executive order to deny illegal migrants the right to seek asylum was an "Obama judge".
"Judges must not legislate security and safety at the border. They know nothing about it and are making our country unsafe," he said in a tweet.
It comes after Supreme Court Chief Justice John Roberts took the unusual step of rebuking Trump's criticism, and said that "We do not have Obama judges or Trump judges, Bush judges or Clinton judges".