Trump's hardline approach on the subject has ramped up tensions and riled Mexicans, who he previously claimed would pay for the construction of a wall between the two countries.
But the leftist Lopez Obrador told reporters in the border state of Sonora on Saturday that angry exchanges were not the answer.
"We are not going to fight with the US government, we are not going to fight with President Donald Trump," he said.
"The migration problem is not resolved by building walls or by use of force, but it's a diplomatic job of respect," added Lopez Obrador, who takes office on December 1.
On Saturday, US authorities announced the start of construction on a five-metre (16-foot) wall along a 6.5-kilometre (4-mile) stretch of the Texan border town of El Paso.
Trump's insurgent campaign for the White House played heavily on a pledge to build a wall on the southern border and to deport millions of undocumented migrants, amid what he claimed was a crisis of immigration.
He initially demanded that Mexico pay for the barrier, a demand Mexico repeatedly rejected. Congress has so far approved $1.6 billion of $25 billion Trump had sought.
Much of the border already has fencing or other barriers, but Trump has ordered a "contiguous, and impassable physical barrier," which scientists say would threaten more than 1,000 species of animals.
Eyewitness? Submit your stories now via social or:
Email: eyewitness@pulse.ng
![Fiona Beal killed her partner and lied to everyone about what happened to him [Northamptonshire Police]](data:image/svg+xml;charset=utf8,%3Csvg%20xmlns%3D'http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg'%20width%3D'300'%20height%3D'172'%20data-ring-placeholder%3D'1'%3E%3C%2Fsvg%3E "Fiona Beal killed her partner and lied to everyone about what happened to him [Northamptonshire Police]")
