The United States and Mexico said on Wednesday that they would move forward with security cooperation to dismantle organized crime groups, focusing on drug-trafficking cartels, and to limit migration while respecting each other’s “sovereignty.”

That seemed to indicate that the Trump administration could limit unilateral cross-border actions against suspected criminals. President Claudia Sheinbaum of Mexico had made clear that any U.S. incursions would be unacceptable.

The announcement came in a joint statement after Secretary of State Marco Rubio met with Ms. Sheinbaum at her office in Mexico City on Wednesday morning, along with Juan Ramón de la Fuente, Mexico’s foreign minister, and its security minister, Omar García Harfuch.

The statement lacked details, except to say that the governments would form a bilateral “high level” group to coordinate actions.

“We both understand that cartels are a threat to the national security of both Mexico and the U.S.,” Mr. Rubio said at a news conference, adding that the governments were engaged in “cooperation that respects the integrity and sovereignty of both countries.”

Mr. Rubio praised Mexico for arresting 59 people whom the U.S. government considers to be “high-value targets” and transporting them to the United States to face drug-trafficking charges.