Hundreds of migrants travelling together in a “caravan” have been prevented from entering the US.
US border officials told some 150 people, many travelling with children, that the Mexico-US border crossing near San Diego was already full.
It was not immediately known whether the migrants from Honduras, Guatemala and El Salvador would be allowed in later or turned back.
President Donald Trump says the caravan is a threat to the safety of the US.
He has vowed to send the US military to secure the country’s southern border with Mexico.
What’s the latest from the crossing?
An organiser told the BBC that no one in the group had been processed by the US Customs and Border Patrol (CBP) at the San Ysidro crossing.
Alex Mensing said about 50 people were still queuing to get into the port of entry while around 100 more were waiting on the Mexican side of the frontier.
In a statement, CBP Commissioner Kevin McAleenan said that “we have reached capacity at the San Ysidro port of entry”.
“Those individuals may need to wait in Mexico as CBP officers work to process those already within our facilities.”
What is this ‘caravan’?
They are a group of asylum seekers, mostly from Honduras.
They set off for the US on 25 March in southern Mexico, near the Guatemala border. The group travelled by bus, train and on foot during their 2,000-mile (3,200km) trek to the US border.
The caravan was organised by US-based Pueblo Sin Fronteras (People Without Borders).
At one point they numbered more than 1,000 people.
Many in the group say they are fleeing from persecution and violence in their countries.
At the scene: The BBC’s James Cook
The patience of the many children among the migrants’ number was striking, although perhaps weariness was the real explanation.
One little girl stood quietly as a woman fixed the child’s hair for an interview at the border which could determine the direction of her life.
A small boy in an oversized checked coat sucked his fingers and gazed around at the crowd as he sat on a man’s shoulders.
President Trump says these families are putting the United States in peril. The migrants insist they are fleeing danger, not bringing it with them.
When is Trump going to build his wall?
Constructing a “big, beautiful wall” along the Mexican border was a signature campaign promise for Mr Trump, but so far the plan to erect a new physical barrier has been thwarted by lawmakers and appears to have stalled.
A major government spending bill which he signed last month included $1.2bn for the border wall – far short of the $25bn the White House sought.
And there were strings attached to the funding Congress did approve. Most of it can only be used to repair stretches of the border where there already is a wall, not to build new segments.
Last month, the Pentagon confirmed Mr Trump had held “initial” talks with Defence Secretary James Mattis about using some of the Pentagon’s budget for constructing a wall.
But Democratic Senators Dick Durbin and Jack Reed wrote to the defence secretary on Monday saying his department had “no legal authority” to use its funds for such a purpose.
In December, US Border Patrol announced arrests at the southern border had fallen to their lowest level since 1971, apparently indicating that fewer people were attempting the crossing.