US border officials have told some 150 migrants, many travelling with children, that the Mexico-US border crossing near San Diego was already full.
Dozens of migrants travelling in a caravan to seek asylum in the United States have now been stopped at the border.
It was not immediately known whether the migrants from Central America would be allowed in later or turned back but the group appears to be staying put.
President Donald Trump says the caravan is a threat to the safety of the US.
The group has been a frequent target for the US president, who has argued in his tweets that it showed the need to tighten immigration laws.
He has asked states bordering Mexico to send troops to shore up security until his proposed border wall is built.
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The caravan set off for the US on 25 March in southern Mexico, near the Guatemala border and at one point numbered more than 1,000 people.
The group travelled by bus, train and on foot during its 2,000-mile (3,200km) trek to the US border, with many saying they were fleeing persecution and violence in their home countries.
What happened at the crossing?
One of the group’s organisers, Alex Mensing, 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.
Some of the members were allowed to cross a long bridge that led to US processing buildings but had to stop outside.
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.”
A lawyer for the group was aghast that inspectors at the border were not ready for them.
“We can build a base in Iraq in under a week. We can’t process 200 refugees. I don’t believe it,” Nicole Ramos told the Associated Press news agency.
