US President Joe Biden and Republican challenger Donald Trump traded barbs over the US-Mexico border during duel trips Thursday -- and as expected, they took clashing tones on the divisive campaign issue.

During his visit to Brownsville, Texas, Biden spoke with border patrol agents and called on his chief political rival to work with his administration and Congress to pass a new $20 billion immigration bill.

"Join me -- or I'll join you -- in telling Congress to pass this bipartisan border security bill," Biden appealed directly to Trump. "We can do this together."

But Trump, who has told Republicans not to support the latest legislation to come before Congress, was having none of it during his visit to Eagle Pass, Texas.

He blamed Biden for the record numbers of migrant crossings into the US and cited several recent cases of violent crimes as examples of "Biden migrant crime."

The two are trying to claim the high ground in the hot-button debate over immigration. A new Gallup Poll shows that immigration has surged to the top as the most important issue on voters' minds.

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