In its own statement, the CBP directly defended its use of tear gas, writing on Twitter that Border Patrol agents "deployed" the substance "to dispel" migrants "because of the risk to agents' safety".
"[CBP] effectively managed an extremely risky situation involving over 1,000 individuals who sought to enter the United States unlawfully in large groups".
"The way things went yesterday".
"I think the funding of the wall right now, never looked better, never looked better", Trump said.
"Far from helping the caravan, they are hurting it", he told the Milenio television network.
But by day's end, the fortified Tijuana-San Diego border crossing was temporarily shuttered as United States border agents and police lobbed tear gas projectiles at migrants, including young children and women on the Mexican side of the border, sparking widespread panic.
The US president's threat comes a day after American authorities closed the country's busiest southern border crossing and fired tear gas into crowds.
Lurbin Sarmiento, 26, of Copan, Honduras, said she had been with her 4-year-old daughter at a concrete riverbed, which had a trickle of water from the Tijuana River, when US agents fired the gas.
"We ran, but when you run the gas asphyxiates you more", Zuniga told the AP while cradling her 3-year-old daughter Valery in her arms.
The wind carried some of the gas toward hundreds of migrants after some tried to get through the wire and fencing separating the two countries.
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As the chaos unfolded, shoppers just yards away on the USA side streamed in and out of an outlet mall, which eventually closed.
For weeks before the 6 November congressional elections, Mr Trump raised the alarm about the migrant caravans and ordered some 5,800 USA troops to the border to support border patrol agents.
The prospective deal between the USA and Mexico was seen as a way to dissuade thousands of Central American migrants from seeking asylum in the US, a process that can take years.
Francisco Vega, the governor of Baja California, said nearly 9,000 migrants were in the state - mainly in Tijuana, with a lesser number in Mexicali - and called it "an issue of national security".
Senior officials of the incoming Mexican government are meeting on Sunday to discuss the plan, according a person familiar with the matter.
Mexico has begun taking steps to increase security near its border with the United States.
Mexican police, some wielding shields, scattered migrants and protesters, many of whom rushed toward the US border.
Irineo Mujica, who has accompanied the migrants for weeks as part of the aid group Pueblo Sin Fronteras, said the aim of Sunday's march toward the USA border was to make the migrants' plight more visible to the governments of Mexico and the U.S.
The groups had initially marched to the border wall from the stadium, Estadio Caliente, in protest and hope they would be permitted to enter, holding signs of U.S. -Mexico-Honduran flags, and others that read, "Donald Trump, Christ loves you", the publication reported.
Scott also said agents only resorted to using tear gas to deter migrants after members began to pelt US officials with rocks.