The federation announced Lozano's departure in a statement, adding, "The Mexican Soccer Federation thanks and recognizes the commitment and dedication of Jaime Lozano. Today his time as Technical Director of the Senior National Team ends."
The federation said it offered a new contract to Lozano through 2030 that included him working under a "more experienced" coach from 2024 to 2026 for the upcoming World Cup to be co-hosted by Mexico, Canada and the United States.
Lozano, under the deal, would have returned at some stage between 2026 and 2030 as the head coach.
The federation said that after Lozano examined the proposal, he "doesn't wish to continue. We respect his decision."
A new national team coach is expected to be named next month.
Lozano, 45, was named interim head coach in June 2023 following the firing of Diego Cocca after a 3-0 loss to the USA in a CONCACAF Nations League semi-final.
Mexico won last year's Gold Cup title under Lozano and last August he was named to stay as the head coach.
Lozano went 10-7 with four drawn in his 13 months guiding the Mexican squad.
In this year's Copa America, a showdown between South American teams and the best from North America, Mexico went 1-1-1 and lost out on the knockout stage to Ecuador by one goal on goal difference.
Mexico beat Jamaica 1-0, lost to Venezuela by the same margin and played Ecuador to a goal-less draw.
