When the Mexican drug kingpin Ismael Zambada García was sentenced to life in prison in a New York courtroom last week, he delivered a message that many Mexican officials found uncomfortable to hear.

Reading his guilty plea aloud, the man known as El Mayo said he had operated freely inside Mexico for years by bribing politicians, the police and the military.

It was not exactly a bombshell — it is well known that Mexican cartels have long thrived by paying off officials. But it underscored a growing problem for President Claudia Sheinbaum of Mexico, who has been under intense pressure from the White House to do more to root out corruption.

For months, Ms. Sheinbaum has tried to manage two complex relationships at the same time: Mexico’s with the United States and her own with her powerful party at home. She has repeatedly said, in essence, that she wants to work with President Trump — but not take orders from him.

She will try to walk that tightrope again in Mexico City on Wednesday, when she meets with Secretary of State Marco Rubio to discuss how to battle the drug cartels.

Mr. Rubio has been one of the U.S. officials highlighting the problem of criminal groups’ power, telling Fox News in March that “in many cases, cooperation is hindered by the dangerous levels of corruption and influence over the judiciary.”