Some 500 migrants from Central America, Venezuela and elsewhere pushed past police and National Guard lines in southern Mexico in one of the first such marches this year.
The migrants described the march as a traditional annual protest related to Holy Week, and those at the front carried a white cross, as others have done in previous years.
In a clash with National Guard officers and immigration agents, the migrants used the cross they were carrying as a battering ram to break through security forces' lines, shattering the wooden cross.
The officers, who had riot shields, batons and what appeared to be an irritant spray, detained some marchers, but many others ran past them.
Migrants have complained they have been essentially confined to Tapachula by the slow processing of their asylum cases and that they are unable to find work in the border state of Chiapas that would allow them to support their families.
"They are practically holding us prisoners; they do not allow us to leave this state because we are not regularized here," said Venezuelan migrant Noreydi Chávez. "They require us to get a visa, but we never get any answers. We fill out paperwork, but they never process it."
The march came as the administration of U.S. President Joe Biden announced it would end a policy that allows turning back asylum seekers on grounds of protecting the country against the coronavirus pandemic.
More than 1.7 million people have been expelled invoking this law since March 2020.
The caravans began several years ago as a way for migrants who did not have the money to pay smugglers to take advantage of safety in numbers as they moved toward the U.S. border.