Eight women and children from a migrant "caravan" have entered the US from Mexico after a two-day stand off with border officials.
Around 150 other members of the convoy are still camped on the border hoping to make their case for entry.
The so-called "caravan" of migrants set off a month ago on a 2,000-mile journey across Mexico to the US border, drawing attention from American news media after President Donald Trump took to Twitter to demand such groups not be granted entry and urging stronger immigration laws.
On Monday Mr Trump said he was "watching" the asylum seekers’ progress closely as his Vice President, Mike Pence, oversaw the rebuilding of a stretch of fence on the border.
US border agents initially refused to admit any of the members, stating their facilities were at capacity.
Celebrations erupted on the border crossing in Tijuana, Mexico, after officials admitted eight women and children, including a nine-month-old baby, fueling the determination of others to remain until they were admitted.
The group was made up of two mothers with one child each, a pregnant woman with two young children, and an 18-year-old man, according to one of the caravan’s organisers.
Separately the US Department of Justice announced it was launching prosecutions against 11 migrants – including members of the caravan – accused of entering the country illegally, four miles west of the border crossing.
"The United States will not stand by as our immigration laws are ignored and our nation’s safety is jeopardised," Jeff Sessions, the Attorney General, said in a statement.
The US has a legal obligation to hear asylum claims – although the majority of applicants from Central America lose their cases. Most in the caravan said they were fleeing death threats, extortion and violence from powerful street gangs in their home countries.
Dozens of them have continued to camp by the border, braving cold desert nights as they await a chance to submit their asylum claims.
"We crossed the whole of Mexico," said Angel Caceres, who said he fled Honduras with his 5-year-old son after his brother and nephew were murdered and his mother beaten and raped. They would stay, he said, "until the last person is in, as long as it takes."
It is not clear when more of the group would be allowed to make their asylum bids. A Customs and Border Patrol (CBP) spokeswoman said the port of entry was congested with other undocumented immigrants, and that the caravan members might have to wait in Mexico temporarily.
Alex Mensing, one of the organizers of the caravan, said no more migrants had been processed since the initial group were admitted around 7pm on Monday evening.
He told the Telegraph: "The whole group now totals about 150 people. About half of them are children and most are from Honduras."
Mr Mensing said the caravan intends to remain on the San Ysidro crossing point for as long as it takes the CBP to process them all, or until the migrants give up.
He stressed that its members have been warned that trying to cross illegally could have serious consequences.
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"The US authorities are illegally turning people away. It is a farce to say that they have no capacity. It is ridiculous. Everyone should be processed immediately…..They have the capacity to pick up large groups in the desert and move them, the detention centers are not full."
"They are trying to focus attention on illegal crossing and at the same time denying people access to the legal process."
Allegra Love, a lawyer from the New Mexico based Santa Fe Dreamers Project, has advised members of the caravan about the lengthy and difficult process.
"The question everybody always has is what will happen…There was frustration and fear because we couldn’t tell them how it will end," she said.