The caravan of Central Americans seeking asylum in the United States sought the world's attention as scores of migrants travelled through Mexico on a journey to escape their violent homelands.

Now that the group has arrived at the Mexico-US border, the next steps in their journey will unfold mostly out of public view.

The caravan first drew attention in the US when President Donald Trump promised that his administration would seek to turn the families away.

But the migrants have been taking turns to keep a constant presence at the entrance of the border crossing.

On Tuesday it was María Magdalena Hiraeta and her family's turn.

When she spoke to AP she was excited, hopeful that this might be the time they get in.

She knew she might be turned around, but was determined to keep on trying.

A total of 28 caravan members were accepted for processing on Monday and Tuesday by US border inspectors at San Diego's San Ysidro crossing, according to an official with US Customs and Border Protection.

For those still in Mexico there is a new hurdle.

Mexico's immigration authorities have asked the migrants to leave the border crossing area and move back to the shelters, citing health concerns, especially for the women and children.

Josue Arevalo, speaking on behalf of the migrants of the caravan, told Mexican officials they will consider moving the women and children, but that most of the men will want to remain at the border crossing.

"I'm not saying 'no' to you now, but the majority of the men will not want to move," he said at a meeting between the migrants and Mexican authorities on Tuesday.