The Mexican foreign ministry pointed instead to places like Honduras, Venezuela, Belize, Colombia and Brazil as countries with higher murder rates, in a statement released yesterday.
Trump had posted earlier: "Mexico was just ranked the second deadliest country in the world, after only Syria. Drug trade is largely the cause. We will BUILD THE WALL!"
He appeared to be referring to a May 9 report from the London-based International Institute for Strategic Studies, which said that Mexico's 2016 murder rate was second only to Syria's.
"It is very rare for criminal violence to reach a level akin to armed conflict," the IISS report said.
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Mexico's foreign ministry acknowledged that the drug trade was "the most important cause of violence in Mexico."
But it described it as "a shared problem that will end only when its root causes are dealt with: the high demand for drugs in the United States and the offer from Mexico (and other countries)."
"We must stop blaming each other," it added.
Mexico had already said in May that the IISS report was based on faulty methodology, saying such comparisons should be based on United Nations crime figures that include central and south American countries.
The wall remains a rallying cry among Trump's supporters, but the proposal -- estimated to cost anywhere from $8 to $40 billion -- has found little support in Congress.
Mexican officials have derided Trump's claim that Mexico will pay for the wall's construction.
Talks with Canada and Mexico to overhaul NAFTA are expected to start in August.