The statement said Mexican authorities had contained the protest at the crossing between Tijuana and San Diego.
It added despite heightened tensions there, Mexico would not send military forces to control 7,417 migrants from a caravan currently amassed at the US-Mexico border.
The situation on the Mexico-US border has become increasingly frantic over the past few hours as desperate migrants attempt to enter the US.
Authorities have resorted to extreme measures to bring the huge so-called “caravan” of people under control.
Tear gas has been fired by US border guards as the migrants attempt to storm the US border.
Tensions have been high in the region since thousands of migrants travelled there after a long journey across the continent.
The migrants – including many children – arrived in Tijuana after travelling more than 4,000km (2,500miles) from Central America.
They claim to be fleeing persecution, poverty and violence in their home nations of Honduras, Guatemala and El Salvador.
Earlier on Sunday an unverified video emerged showing scores of migrants breaking through a border fence in the area.
The migrants were then reportedly pushed back using tear gas.
Traffic was suspended in both directions at the San Ysidro port of entry.
But a major section of the crossing has now been reopened, with the Customs and Border Protection of San Diego saying: “Pedestrian East and West are open at the San Ysidro port of entry for both northbound and southbound crossings.”
The US Department of Homeland Security (DHS) recently issued a statement in response to the worsening situation
It read: “Migrants attempted to breach legacy fence infrastructure along the border & sought to harm CBP personnel by throwing projectiles at them.
“DHS will not tolerate this type of lawlessness.”
Mexican police in high visibility jackets were deployed in response to the crisis.
Crowds above the police could be seen in online video footage shouting on a bridge near the crossing.
Trump has repeatedly railed against the so-called “caravan” of migrants, warning of “illegal aliens” approaching the US in blistering anti-migrant rallies.
The President deployed troops to the border to add support to the Border Patrol.
Trump blamed the huge migrant influx on his Democratic foes and implored Mexico to play its part in policing it.
On Saturday the he tweeted: “Would be very smart if Mexico would stop the caravans long before they get to our Southern Border, or if originating countries would not let them from (it is a way they get certain people out of their country and dump in US. No longer).
“Dems created this problem. No crossings!”
More to follow…