"Mexico is going to become a power - and will change the balance of power. Nobody will threaten us that our borders will be closed or militarised," warned Lopez Obrador, who takes office December 1.
"This will be possible because the country will grow and there will be jobs."
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Trump has cited Mexico's record number of homicides last year as one of many reasons the United States needs a more secure border.
The reality star turned president campaigned on a promise to deport undocumented immigrants and build a new border wall with Mexico -- which he said would be paid by America's southern neighbor - to prevent arrivals of undocumented migrants, whom he has described as criminals.
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Trump's explosive remarks cost him business contracts and fueled the worst diplomatic crisis in decades between the United States and Mexico.
On May 14, a senior US delegation led by Secretary of State Mike Pompeo met with Lopez Obrador in Mexico City.
But the issue of the wall was not addressed then or in letters that the Mexican president-elect later exchanged with Trump.
Official Mexican government statistics counted 28,711 murders in 2017, the highest since records began in 1997.
The situation has worsened, with another 15,973 murders over the first half of this year alone.
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