The president could sign a treaty with Mexico agreeing to ban the manufacture, importation and sale of assault weapons inside the United States of America. Needing only the approval of the Senate, the administration could legally bypass the House of Representatives, without having to issue an executive order.
Since over 50,000 Mexicans have already signed a petition asking the US to ban these weapons and the president of Mexico has repeatedly complained about the smuggling of these types of weapons into Mexico by drug gangs, getting approval of the Mexican government shouldn't be a problem.