Members of the Jalisco New Generation Cartel (CJNG), one of the most powerful and feared criminal organisations in Mexico, have torched businesses and erected burning blockades since El Mencho’s death.
The Mexican Open issued a statement saying “the supposed cancellation of the event due to security issues in Jalisco is false”.
It said: “The event continues as scheduled and tournament operations are proceeding normally.
“We remain in coordination and constant communication with federal, state, and municipal authorities, under the established security protocols.”
Britons Katie Boulter and Heather Watson are scheduled to compete in the Merida Open in Mexico this week.
The event takes place in the state of Yucatan, which does not appear to have been significantly affected by the violence.
The WTA said increased police presence and additional security measures have been put in place at the tournament following the incidents in Jalisco, which is about 1,000 km away.
“The safety of players, staff, and spectators remains our top priority,” the women’s governing body told BBC Sport.
“The tournament is operating as scheduled and there have been no reports of incidents in the region.”
Boulter plays Brazil’s Beatriz Haddad Maia on Monday and Watson faces Spaniard Jessica Bouzas Maneiro on Tuesday.