Tijuana, Mexico (CNN) Busloads of Central American migrants arrived in this Mexican border city on Tuesday. And more are coming.

But it will likely be days before members of the group -- which organizers say is about 600 people in total -- head to the US-Mexico border to turn themselves in and ask for asylum.

They're part of a caravan that convened at Mexico's southern border weeks ago, then trekked through the country as part of an annual pilgrimage organized to bring light to the plights of migrants.

A large number of people in this year's caravan are from Honduras. Among the reasons they've given CNN for fleeing the country: widespread gang violence, domestic violence, poverty, political repression after a contested presidential election and discrimination against the transgender community.

US officials have already made it clear they're skeptical of the migrants' motives, warning that anyone with an invalid claim will be swiftly deported and that anyone who tries to cross the border illegally will face prosecution.

Migrants in the caravan wait for buses to take them from Hermosillo, Mexico, to the next stop on their journey.