A surreptitiously taped video clip that surfaced Tuesday shows the mayor of Mexico’s busiest cargo port seemingly receiving instructions from the chief of the Knights Templar crime group, underscoring how deeply the organization has co-opted politicians in troubled Michoacan state and what a difficult task it will be for authorities to restore the rule of law there.

Arquimedes Oseguera, the mayor of the port of Lazaro Cardenas, was arrested Monday, and a federally appointed overseer of security in the state of Michoacán said it was because of his links to Servando Gomez, a crime boss often called by his nickname, “La Tuta,” or “professor.”

It wasn’t until Tuesday, though, that the extent of those links became apparent. The video clip, posted on YouTube, shows Mr. Oseguera at an open-air table with Mr. Gomez. At least five other men are present, including, according to the Quadratin news portal, Jose Guadalupe Jaimes Valladares, a former mayor of Apatzingan, an agricultural hub in Michoacan that served as a Knights Templar stronghold before federal forces took over the state earlier this year.

Oseguera is the third mayor federal forces have arrested this month.

“I support you, you bastard, in whatever you want,” Gomez is heard telling Oseguera, a politician of the leftist Party of the Democratic Revolution.

In other moments, Gomez stands over Oseguera and appears to give him instructions, although the dialogue is not clear.

Lazaro Cardenas, a port city of 160,000 people on Mexico’s Pacific coast, is the busiest port in Mexico and one of the biggest along the Pacific coast of the Americas, handling 25 million tons of cargo annually. Controlling it allows the Knights Templar to ramp up traffic in narcotics and synthetic drugs.

Fighting to halt the slide of Michoacán into lawlessness, President Enrique Peña Nieto sent federal police and soldiers into the state in mid-January. Since then, federal forces backed by armed vigilante militias have killed or arrested three of the four most prominent Knights Templar bosses, leaving only Gomez on the lam.

The Knights Templar’s presence in Michoacán became so pervasive that vigilante groups rose up in anger, beginning in February 2013, to halt its extensive extortion demands on business owners, transport companies, and mining interests.

The vigilante groups have grown dramatically over the past year and now present a problem themselves. The Peña Nieto government walks a tightrope in dealing with them, using their on-the-ground knowledge to root out Knights Templar drug lords while worrying that hundreds, if not thousands, of the vigilantes might turn to crime themselves.

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Last Friday, militia leaders signed an agreement with Alfredo Castillo Cervantes, the Peña Nieto-appointed security chief for Michoacán, that obligates vigilantes to register their weapons with the army by May 10. An undetermined number will be allowed to keep rifles but not to carry them in public.

More than 500 militia members have signed up for a new Rural Defense Corps under the control of the army.