The veteran leftist leading in the polls for the July 1 election, Andres Manuel Lopez Obrador, vowed that if he wins, Mexico will no longer be the United States's "pinata."
"We are going to be very respectful toward the United States government, but we are also going to demand that (the United States) respect Mexicans," he told a cheering crowd as he kicked off his campaign in Ciudad Juarez, on the US border.
"Neither Mexico nor its people will be the pinata of any foreign government."
The comment came after Trump's latest series of vitriolic anti-Mexican tweets, in which he threatened to pull the United States out of the North American Free Trade Agreement (NAFTA) unless Mexico does more to stop cross-border drug trafficking and illegal migration.
"They must stop the big drug and people flows, or I will stop their cash cow, NAFTA. NEED WALL!" he wrote.
Lopez Obrador, a former Mexico City mayor, repeated his long-standing criticism of Trump's planned border wall.
"Let this be heard near and far: neither security issues nor social problems can be resolved with walls or the use of force," he said.
"But we're not ruling out the possibility of talking Donald Trump out of his mistaken foreign policy and, in particular, his contemptuous attitude toward Mexicans," he said.
The second-place candidate in the Mexican presidential race, Ricardo Anaya of the conservative National Action Party (PAN), also hit out at Trump.
"We will maintain a strong and dignified stance in the face of the US president's latest statements," he said ahead of a rally in the town of San Juan de los Lagos, in the western state of Jalisco.
"We need a new relationship of shared responsibility and mutual respect."
Recent polls give Lopez Obrador just over 40 percent of the vote as the campaign opens for Mexico's single-round election, with Anaya in the 20s, closely trailed by Jose Antonio Meade of the ruling Institutional Revolutionary Party (PRI).
Mexican Foreign Minister Luis Videgaray also reacted defensively to Trump's tweets.
"Every day Mexico and the US work together on migration throughout the region. Facts clearly reflect this," he wrote on Twitter, concluding with what appeared to be a tongue-in-cheek "Happy Easter."
