The White House on Wednesday batted down suggestions from some Republican lawmakers to designate Mexican drug cartels as terrorist groups in the wake of the deadly kidnapping of four Americans, arguing it would have minimal benefits.

“Designating these cartels as [foreign terrorist organizations] would not grant us any additional authorities that we don’t really have at this time,” press secretary Karine Jean-Pierre said at a briefing with reporters. “The United States has powerful sanctions authorities specifically designated to combat narcotics trafficking organizations and the individuals and entities that enable them. So, we have not been afraid to use them.”

She noted that the Treasury Department has taken a series of actions sanctioning various Mexican companies and individuals connected to the drug trade in recent months. 

Last October, the department sanctioned transporters involved in the Sinaloa cartel’s drug trafficking operations, sanctioned multiple individuals and entities last month who were part of the meth and fentanyl trade, and last week targeted eight Mexican companies linked to timeshare fraud on behalf of the CJNG, a Mexico-based cartel that traffics fentanyl and other drugs. 

Jean-Pierre’s defense of the administration’s strategies came in the wake of a violent incident just south of the U.S.-Mexico border.

Four Americans were kidnapped by armed men last Friday after crossing the border for a trip to get a medical procedure. Two of the Americans were found dead on Tuesday. The two others arrived back in the U.S. on Tuesday and began receiving medical treatment.

The White House has called the killings “unacceptable” and said the administration is working with Mexican officials to learn more about the incident. 

Republicans have responded by calling for a tougher approach to the drug trade in Mexico. 

Advocates argue that designating a group as a foreign terrorist organization would provide additional resources for prosecution and give greater authority to freeze financial assets.

Sen. Lindsey Graham (R-S.C.) spoke Wednesday about legislation that would classify certain Mexican drug cartels as terrorist organizations, describing them as a national security issue. Graham said Sen. John Kennedy (R-La.) would join forces on the measure, and he suggested at least some Democrats would be involved.

“An FTO designation is the highest designation you can give a criminal terrorist enterprise that’s not a nation-state,” Graham said, citing nine different cartels that he argued would warrant the designation.