MEXICO CITY—The arrangement at first seemed simple: Harvard University would give Mexico's departing leader a one-year fellowship to do some research there.

But ex-President Felipe Calderón's position has sparked controversy over whether the prestigious institution should open its doors to a man whose war against drug traffickers led to tens of thousands of deaths during his six-year term, which ended Dec. 1.

Felipe Calderón, the former president of Mexico, pictured in 2011. Bloomberg News

The debate isn't taking place at the hallowed halls of Cambridge, Mass., but here in Mexico, where the lectureship Mr. Calderón started Monday has vaulted him back to the front pages of newspapers, to the top of radio hours, and to talk among ordinary Mexicans.

Two top Mexican activists wrote an open letter to a Harvard dean questioning the appointment. A pair of petitions posted on website have generated about 34,000 signatures of mostly Mexicans who object to Harvard's offer and accuse Mr. Calderón of waging a reckless drug war. The petitions' organizers presented them to the Harvard president Tuesday.

A conservative lawyer, Mr. Calderon earned praise for being the first president to aggressively take on drug gangs and capture and kill top barons. But at least 60,000 other Mexicans were killed, and an estimated 25,000 are still missing.

Two organizers of a petition questioning Calderón's Harvard appointment. Reuters

In a statement, Mr. Calderón's spokesman defended the ex-president, saying he "did the right thing, he fought crime as never before, began a process of rebuilding law enforcement institutions that was necessary to reverse a process of corruption that was destroying them." He blamed past attacks and the Harvard imbroglio on "radical critics and opponents."

The backlash seems to have taken Harvard by surprise. Many professors there laud Mr. Calderón's achievements and say he is a moderate and a far cry from Latin American strongmen of yesteryear. They argue Mr. Calderón faced difficult choices and even made mistakes—but that is the very material of debate at an institution like Harvard.

"A university that only appoints people who agree with each other should shut down," said Jorge Domínguez, who teaches courses on Mexican government there. "We intend to remain open for a future of continuing vigorous debate, research and education."

The university said Mr. Calderón, who got a master's degree from Harvard's John F. Kennedy School of Government in 2000, is a well-known alumnus and a natural fit. Spokesman Doug Gavel said the former president was highly recommended by a faculty panel and the university is sticking by its decision.

Mr. Calderón also has defenders in Mexico, too. Tatiana Clouthier, a political commentator and former member of Mr. Calderón's Conservative Party, wrote in an editorial: "What's sad is people don't see the good he's done, for all the recent bloodshed and pain."

Mexican presidents have a long history of going abroad, even to teaching jobs, after rocky times at home following their presidencies. Ernesto Zedillo was widely scorned by his party after he spearheaded electoral reforms that broke its seven decades of rule when his presidency finished in 2000. He decamped to Yale University. His predecessor, Carlos Salinas, dogged by corruption scandals, went into a self-imposed exile in Ireland; he has since returned to Mexico.

Some critics of Mr. Calderón's appointment say the former president still owes Mexicans answers on casualties. Throughout his term, Mr. Calderón said that 90% of the dead were criminals caught in internecine fighting. But prosecutors said they left large numbers of cases uninvestigated.

During his last year, Mr. Calderón refused to disclose the number of drug-related deaths.

Some critics also say the military carried out human-rights abuses in pursuing drug gangs, including torture and disappearances. More than 7,000 complaints have been filed with Mexico's government ombudsman, alleging crimes from robbery to killings by soldiers; several dozen soldiers were convicted of crimes during Mr. Calderón's term in the military's own courts. The military says it is investigating others.

"For Harvard to give him this position is for them to be openly backing his policies—which created nothing but disaster for Mexicans during the six years," said Eduardo Cortés, who owns a construction firm in Puebla and started one of the online petitions.

Sergio Aguayo, a left-leaning academic who wrote the open letter to Harvard, complained that Mexicans still lack closure on the more than 25,000 disappearances which remain unsolved during his term. He said he hoped that his successor Mr. Peña Nieto will get to the bottom of what happened to these people.

Mr. Aguayo stopped short of asking Harvard to disinvite Mr. Calderón. "We're just looking for better answers on why he was chosen," he said.

The dispute highlights the extent to which Mr. Calderón has become the public face of Mexico's battle against drug gangs—which existed long before he took power in 2006. Even Mexico's new President Enrique Peña Nieto has tried to distance himself from some of his predecessor's strategies since taking office last month, promising to reduce the country's homicides and violent crime.

Steven Levitsky, a Harvard government professor, said the Kennedy School has made some mistakes when dealing with Latin American leaders. In the 1990s, it allowed Guatemalan Gen. Héctor Gramajo to study for a master's degree. Mr. Gramajo was accused of torture by human-rights groups and his U.S. visa was eventually revoked.

But Mr. Levitsky said it was ridiculous to put Mr. Calderón in the same category as the military leaders that waged war against political opponents, when Mr. Calderón's fight was directed squarely at crime groups threatening the rule of law. "No one considers Calderón to be an extremist," Mr. Levitsky said.

Write to Nicholas Casey at