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The policy had led to nearly 2000 children - some as young as 8 months old - being separated from their parents and held in detention centres in just six weeks.
Mr Trump previously had insisted his hands were tied on the zero tolerance policy regarding illegal border crossings, condemned in the United States and worldwide.
But early on Thursday morning (NZ time), the president said he was now prepared to sign an executive order on immigration ending the immediate separation of immigrant families at the US-Mexico border.
American expatriate Sonia Voldseth had organised a protest against the policy in Queenstown for Sunday, saying it was "abhorrent" and children should not be used as "political pawns".
Ms Voldseth told the Otago Daily Times this morning this would not go ahead.
However, she has called for donations to the organisations Together Rising (togetherrising.com), ACLU (aclu.org), and Raices Texas (raicestexas.org).
Donations were key as "the journey for these families is not over'', she said.
- additional reporting by Reuters