TIJUANA, Mexico (Reuters) - At least 88 Central American asylum seekers from a caravan through Mexico had crossed into the United States by Wednesday, a movement that prompted U.S. Attorney General Jeff Sessions to beef up legal resources on the border.

Dozens more remain just outside the entrance to the port of entry in a makeshift camp, waiting to plead their case.

Women, children and transgender people were among those who waited for hours inside the walkway to the U.S. gate before being allowed to pass through to begin the asylum process.

Those remaining wandered among boxes of cereal and diapers in a labyrinth of giant tents, near-luxury conditions for the bedraggled migrants, compared to the scarcity they had endured for weeks on their journey through Mexico to the U.S. border.

On Wednesday, U.S. officials let in three groups totaling 63 migrants, a dramatic uptick from the trickle permitted since Monday.

Border officials had allowed through only a few at a time, saying the busy San Ysidro crossing to San Diego was saturated and the rest must wait their turn.

In response, the Justice Department was sending 35 additional assistant U.S. attorneys and 18 immigration judges to the border, Sessions said, linking the decision to the caravan.

“We are sending a message worldwide: Don’t come illegally. Make your claim to enter America in the lawful way and wait your turn,” he said, adding that he would not let the country be “overwhelmed.”

Despite unusual attention on the annual, awareness-raising caravan after President Donald Trump took issue with it last month, the most recent data through December does not show a dramatic change in the number of Central Americans seeking asylum.

Apprehensions of people crossing to the United States illegally from Mexico were at their highest in March since December 2016, before Trump took office.

More than 100 members of the caravan, most from Honduras, Guatemala and El Salvador, have been camped in the square near the entrance of the San Ysidro pedestrian bridge from Mexico to the United States, waiting for their turn to enter the checkpoint.

PLEADING THEIR CASE

At least 28 migrants who made it into the United States on Wednesday had anxiously filed through the walkway to the U.S. gate the night before. Two by two, they walked up to a U.S. Customs and Border Protection officer standing in the gate to ask if they might pass through.

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First to try was a man and his small nephew, a football under his arm; then a mother and child; then a woman with her grandsons.

Throughout the caravan’s 2,000-mile (3,220-km) odyssey from southern Mexico, its members maintained hope they would ultimately get the chance to plead their case for asylum in the United States, all the while knowing that U.S. officials might reject them.

The Trump administration cites a more than tenfold rise in asylum claims versus 2011 and growing numbers of families and children, who are more likely to be allowed to remain while their cases await hearing, as signs that people are fraudulently taking advantage of the system.

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Trump wants to tighten laws to make it harder for people to claim asylum. For now, though, despite his orders to keep such migrant caravans out of the country, international and U.S. law obliges the government to listen to people’s stories and decide whether they deserve shelter.

The U.S. Department of Justice said on Monday it had launched prosecutions against 11 “suspected” caravan members on charges of crossing the border illegally.

Nicole Ramos, an attorney advising caravan members in Mexico, said she did not believe the individuals facing U.S. criminal charges were part of the caravan group.

“Quite a few people have claimed to be part of the caravan, including a sizeable contingent of Guatemalan men who were never part,” Ramos said.