Gathered at a park in the border city of Ciudad Hidalgo, the migrants voted by a show of hands and then marched to the bridge to urge those still there to cross the river and join them.

"Let's all walk together!" and "Yes we can!" they cried, defying warnings to turn back this week from US President Donald Trump, who has sought to make the caravan and border security in general into a campaign issue a little over two weeks before midterm elections.

The group's decision capped a day in which Mexican authorities again refused mass entry to migrants on the bridge, instead accepting small groups for asylum processing and giving out 45-day visitor permits to some of them.

Mexico had sought to maintain order after a chaotic Friday in which thousands rushed across the bridge only to be halted by a phalanx of officers in riot gear. Authorities began handing out numbers for people to be processed in a strategy seen before at US border posts when dealing with large numbers of migrants.

But despite a continued heavy police deployment on the bridge, a steady stream of migrants made it to Mexican soil with relative ease by crossing the Suchiate River that demarcates the notoriously porous border.

They swam, waded with the aid of ropes or paid locals to ferry people and goods across the muddy waters, and were not detained on reaching the Mexican bank.

Australian Associated Press