Videgaray acknowledged they had no firm agreement but said both sides had a better understanding of the magnitude of the drug crisis.
Tillerson said drug trafficking had to be addressed as a "business model," attacking cash flow, gun procurement, production and distribution.
Mexicans long have argued that U.S. counternarcotics strategies have failed to focus on the demand side: U.S. addicts and recreational users consuming huge amounts of cocaine, heroin and marijuana that is smuggled in from Mexico by violent drug cartels.
That, Tillerson said, must change.
"But for us," Tillerson said, "Mexico wouldn't have the trans-criminal organized crime problem and the violence that they're suffering. ... We really have to own up to that."
Tillerson was joined by Homeland Security Secretary John Kelly, and both sought to emphasize a willingness to cooperate with Mexico despite strained relations at the start of the Trump administration.