The standoff at the border threatens to become the first crisis for Mexico’s president-elect, Andrés Manuel López Obrador, who takes office on Saturday. His government will be forced to navigate demands from Washington to deal with the migrants — at the same time that it faces deepening concern from Mexican border communities straining to house and feed thousands of impoverished and increasingly desperate guests.

Soon after the migrants began their mid-morning march to the border in Tijuana, they were met by Mexican federal police officers at a bridge that leads to the San Ysidro border crossing, through which millions of people and vehicles pass each year. At that point, many of the marchers bypassed the police by running across a dry riverbed.

The police, carrying riot shields, formed a new line and appeared to contain the rush of migrants 100 yards or more from the crossing. They erected metal barriers on the roads and sidewalks leading to the main border crossing for cars and trucks.

A smaller group of migrants then tried to make their way to a train border crossing a few hundred yards away, where they were stopped by tear gas fired by United States Customs and Border Protection officers.

After the gas cleared, Mexican federal police officers pushed the protesters back from the area of the train crossing.

Customs and Border Protection officers also used tear gas at a separate point a few hundred yards away from the train crossing to drive back the migrants.

Some of the migrants told The New York Times they thought they could negotiate with United States officials to be allowed to pass. A few men tried to climb the wall but fell back in the face of the gas.

At least two dozen tear gas canisters could be seen on the Mexican side of the border after the migrants eventually turned back.

Senator Brian Schatz, Democrat of Hawaii, writing on Twitter, said, “Tear gas across the border against unarmed families is a new low.”

Kirstjen Nielsen, the Homeland Security secretary, said in a statement that some migrants who were trying to breach the fence had thrown projectiles at Customs and Border protection workers.

“As I have continually stated,” she said, “D.H.S. will not tolerate this type of lawlessness and will not hesitate to shut down ports of entry for security and public safety reasons.”

Customs and Border Protection officers are trained in the use of tear gas for crowd control and have used pepper spray at the border before.

Mexico’s interior ministry said that 500 people were involved in the march on Sunday, a fraction of the total number in the caravan that left Honduras and headed north last month, and that those who had attacked federal police would be deported. Municipal officials said that 39 people had been arrested.

The unrest in Tijuana comes amid broader discussions about how to deal with the growing number of migrants fleeing poverty and violence in Central America who are amassed at crossing points in Tijuana and elsewhere along the border.

The backlog of people waiting to request asylum at a checkpoint has swelled, causing frustration among the migrants to boil over. Some of those rushing the border on Sunday had children in strollers and in their arms.

“The longer the caravaners stay in Tijuana, the more likely they are to succumb to the temptation to cross illegally into the U.S.” said Wayne Cornelius, professor emeritus of political science at the University of California, San Diego, who is an expert on the border.

A migrant family running away from tear gas near the border wall between the United States and Mexico in Tijuana on Sunday.CreditKim Kyung-Hoon/Reuters