Authorities on the US side used tear gas to disperse the would-be crossers, the journalists told CNN.
On Sunday, Mexico promised to shore up security along the border, and the country's Interior Ministry said it would immediately deport those who tried to "violently" enter the U.S. from Tijuana.
Honduran Ana Zuniga, 23, said she saw other migrants open a small hole in concertina wire at a gap on the Mexican side of a levee, at which point USA agents fired tear gas at them.
"The people of Tijuana will not pay for the stay of these migrants".
On Sunday, hundreds of caravan members, including women and children, were peacefully protesting when they were stopped by Mexican authorities, who told them to wait for permission.
Stephanie Leutert, director of the Mexico Security Initiative at the University of Texas at Austin, described the Remain in Mexico plan as a strategy to take away the ability of migrants to live and work in the US while cases are processed.
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But, Trump said, "whether he did or whether he didn't, he denies it vehemently". He later told reporters that "nobody's done more for the military than me".
The incident took place at the Ysidro Land Port of Entry between Tijuana and San Diego, where tens of thousands of people cross between the us and Mexico each day.
In recent weeks, thousands of mostly Central American migrants have arrived in Tijuana by caravan.
Video clips posted on Twitter showed large numbers of migrants dashing across a shallow concrete waterway toward the border.
Children screamed and coughed in the mayhem of the tear gas.
"It is critical that we demonstrate the mass sentiment in support for migrants and refugees, and demand the recognition of their legal right to seek asylum", they say.
With bridge and pedestrian border crossings closed in both directions, the migrants headed for the cargo area where the railroad crosses, Alvarez said. About 100,000 people cross there each day.
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In their, Konkani-style wedding , Deepika was dressed in a red and gold Sabyasachi saree , while Ranveer wore a white kurta. The first of Deepika and Ranveer's guests began to arrive at the Leela Palace, where their reception is being hosted.
Customs and Border Protection officers also released tear gas at a separate point a few hundred yards away to drive back the migrants. "From travel to shipping to daily commutes between San Diego and Tijuana, it is essential to our community".
Trump has repeatedly warned that the large group of migrants moving through Mexico toward the United States included criminals and possibly terrorists, while providing no evidence to support that.
On Sunday, Trump took to Twitter Sunday to express his displeasure with the caravans in Mexico.
"They are doing things outside of the law", he wrote. Tijuana's mayor declared the situation a humanitarian crisis. Most of the migrants are being housed at a sports complex, where they face long wait times for food and bathrooms.
But Mexico's incoming government, which assumes power December 1, denied that it is willing to let USA asylum-seekers stay there pending the outcome of their cases in US immigration courts, which could take years. "We want to see if they'll give us permission to go to the USA", she said.
Junior, a migrant from Honduras, waves the American flag while standing with other migrants at the US-Mexico border fence.
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Donald Trump used the issue to call for Clinton to be jailed , which led to rally chants of "Lock her up". Ivanka in the past had said that she was not familiar with some details of the federal records rules.