Tijuana (Mexico) (AFP) - Hundreds of Central American migrants staged a boisterous demonstration on the US Mexico border Thursday, screaming for President Donald Trump to let them in as US soldiers and riot police put on a menacing show of force.

The increased tension over the presence of a thousands-strong migrant caravan came as Trump marked Thanksgiving Day by threatening to close the border if he thinks Mexico has lost control of it.

Vehicle and pedestrian traffic at the busy San Ysidro crossing came to a halt for 40 minutes as dozens of US police wearing helmets and holding rifles formed a line facing the Mexican side of the frontier. Separately, riot police rehearsed deployment movements. US Customs and Border Protection called all of this a "large-scale readiness exercise."

American soldiers in khaki-colored uniforms set off rockets that exploded with a pungent-smelling white smoke. Helicopters hovered overhead.

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Trump has already deployed nearly 6,000 troops along the border and on Thursday he threatened to go even further.

"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," Trump told reporters, before firing a warning to Mexico.

"The whole border. I mean the whole border," he said, adding that "Mexico will not be able to sell their cars into the United States."

At almost the same time as the police and troop exercise, at another nearby border crossing called El Chaparral, Central American migrants from the caravan emptying into Tijuana defied the president with a loud rally.

"Open the gates, Trump! We are not looking for war, but work," shouted Alberto Ruiz, a 22-year-old Honduran.

After a trek of more than a month from Honduras, nearly 5,000 migrants have been living in a makeshift shelter fashioned from an open air sports arena. It rained Wednesday night, drenching their mattresses and other belongings.

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"Let's go to the border! There we can pressure Trump. We are only wasting time and strength at the shelter," Carlos Rodriguez, also Honduran, yelled into a bullhorn.

- 'A special day' -

"Today is a special day. It is Thanksgiving in the United States. They are not going to lynch us," he said as a crowd applauded and screamed in support.

As the chill of night set in, dozens of migrants lugged their wet belongings from the shelter and set up a new camp right in the middle of a street near the El Chaparral crossing.

Authorities in Tijuana have set up a job fair in an attempt to recruit skilled workers from among the migrants for the benefit of local companies, while Mexico's migration agency has offered them temporary residency papers.

Some have taken advantage of the offers but others are simply determined to reach the US.

Since setting out more than a month ago, mostly from Honduras, thousands of migrants -- including many women and children -- have covered about 4,400 kilometers (2,700 miles), either walking or hitchhiking, before the first groups began reaching Tijuana at the end of last week.

But there have been tensions since they started arriving at the border town, with some locals fearing crime and violence.

The migrants are mostly fleeing poverty and unrest in Central America's "Northern Triangle" -- El Salvador, Guatemala and Honduras, where gang violence has fuelled some of the highest murder rates in the world.