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 BBC reported.
Mr 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 United States where they make so many cars,” he added.
Mr Trump’s reference to lethal force appeared to contradict assurances given by Defence Secretary James Mattis that 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.
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 of rebuking Mr Trump’s criticism, telling the Associated Press that “We do not have Obama judges or Trump judges, Bush judges or Clinton judges”.
Almost 3,000 Central American migrants have arrived in the Mexican border city of Tijuana after crossing Mexico and parts of Central America. More than 2,750 have sought refuge in a shelter set up by the mayor’s office.
US officials have warned that anyone found entering the country illegally will face arrest, prosecution and deportation.
The migrants say they are leaving their respective countries in the hope of building a better future for themselves and their families.
Some say they have been threatened or mistreated by criminal gangs operating in their hometowns. Many are travelling with their children whom they do not want to fall prey to the gangs.
ALSO READ: Numerous deaths as boat capsizes off Cyprus
Others hope to get jobs abroad which pay enough for them to send money to their relatives who stayed behind.
Many say their dream is to reach the US. Some of them have relatives there already whom they hope to join; others have chosen it as their destination because they think they will earn higher salaries there than in Latin America.
While Central Americans have long fled their homelands for the US and have sometimes joined forces along the way, the organised nature of this caravan is relatively new.
Migrants are often kidnapped by people traffickers and drugs gangs which force them to work for them. A large group such as this one is harder to target and therefore offers more protection.