The group, which includes two former U.S. ambassadors to Mexico, also said the U.S. should do more to stop the smuggling of firearms and ammunition into Mexico by stepping up investigations of gun dealers and more strictly regulating gun shows.
The Binational Task Force on the United States-Mexico Border listed the assault weapons ban as a step the U.S. should take immediately to improve security in both countries. The last ban expired in 1994.
"Improving our efforts ... will weaken the drug cartels and disrupt their illegal activities, and make it easier ultimately to dismantle and destroy them," said Robert Bonner, co-chairman of the group and former head of both the U.S. Drug Enforcement Administration and Customs and Border Protection agency.
U.S. and Mexican officials say drug cartels frequently use assault rifles, which are banned in Mexico but easily purchased in the United States.
Mexican President Felipe Calderon launched a nationwide crackdown on drug cartels when he took office in December 2006. The offensive has been met with unprecedented violence, leaving more than 13,800 people dead.
During his run for office, President Barack Obama promised to push to reinstate the ban. He has since said he would rather enforce existing laws that make it illegal to send assault weapons across the border.
Other recommendations related to border security included restructuring Mexico's law enforcement operations to create a counterpart to the U.S. Border Patrol, increasing U.S. assistance to Mexico to build up law enforcement and reducing demand for drugs in the United States through more treatment programs.