American law enforcement officials spent years looking into allegations that allies of Mexico’s president, Andrés Manuel López Obrador, met with and took millions of dollars from drug cartels after he took office, according to U.S. records and three people familiar with the matter.

The inquiry, which has not been previously reported, uncovered information pointing to potential links between powerful cartel operatives and Mexican advisers and officials close to the president while he governed the country.

But the United States never opened a formal investigation into Mr. López Obrador, and the officials involved ultimately shelved the inquiry. They concluded that the U.S. government had little appetite to pursue allegations against the leader of one of America’s top allies, said the three people familiar with the case, who were not authorized to speak publicly.

Mr. López Obrador called the allegations “completely false,” responding to questions from The New York Times on Thursday. He said the news of the inquiry would not “in any way” affect Mexico’s relationship with the United States, but said he expected a response from the U.S. government.

“Does this diminish the trust the Mexican government has in the United States?” Mr. López Obrador said at a regular news conference, adding, “Time will tell.”

Drug cartels have long infiltrated the Mexican state, from the lowest levels to the upper reaches of government. They pay off the police, manipulate mayors, co-opt senior officials and dominate broad swaths of the country.