The deaths occurred near Mexico City's central Paseo de la Reforma, where about one million people gathered to celebrate Mexico's 2-0 win over Ecuador in the previous round, which was the team's first World Cup knock-out win in 40 years.
"We must avoid alcohol abuse, because whenever there is excessive drinking at these kinds of celebrations, problems can arise, including more violence linked to alcohol," Sheinbaum said at her regular morning press conference.
She also called on supporters to avoid overcrowded areas, saying fans and authorities alike share responsibility for ensuring celebrations remain safe.
Three of the victims in the capital - a 44-year-old man and two women, aged 19 and 48 - died of suffocation after being crushed in the crowd, authorities said.
Mexico face England at the Estadio Azteca on Sunday, July 5th (Monday, July 6th, at 02.00 CEST) in the round of 16.
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