Washington, Apr 30 (IANS): Dozens of asylum-seeking migrants have reached the US-Mexico border after a month-long journey from Central America, vowing to remain outside an immigration processing centre until "every last one" is admitted into Washington, the media reported.

Alex Mensing, an organiser with Pueblo Sin Fronteras which assembled the caravan, on Sunday said 50 migrants were admitted to the centre on the Mexico side, reports CNN.

The migrants marched from Friendship Park in Tijuana, Mexico to the San Ysidro port of entry on Sunday.

They stood on the Mexican side; on the other side lay San Diego, California. It was the final leg for some in the caravan of hundreds of migrants, which had reached Tijuana on April 24.

Mensing said the migrants' decision to not return to a nearby shelter overnight was made in solidarity with the asylum seekers who are inside the facility.

However, the fate of the migrants remain uncertain.

Before the group arrived on Sunday, US Customs and Border Protection officials said the port had already reached full capacity, and migrants trying to get into the US may need to wait in Mexico as officials process those already in the facility.

Some migrants said they had walked the last leg of the journey filled with anxiety. Others scarfed down food before they filed into the centre, afraid there would be no food once they turned themselves in to border officials.

One woman in a wheelchair told CNN that she did not know where she was going, just that she was going to the US.

The caravan is both a humanitarian and an activist mission, as organisers created the event to draw greater attention to the migrants' plight.

Last week, President Donald Trump encouraged Mexico to break up the caravans and said that he would not accept the migrants into the country.

It is not illegal to enter the country at a port of entry and ask for asylum, as international law requires that the US consider asylum claims.

The migrants say they were not planning to sneak across the border, but to turn themselves in peacefully and ask for asylum.