It has now suffered at least 46,688 deaths during the pandemic, with a total of 424,637 infections.
Previously the United Kingdom had the third highest toll, and registered 46,204 deaths as of Friday.
The World Health Organization (WHO) has warned the effects of the pandemic will be felt "for decades to come".
In Mexico, local authorities have previously said they believe the real number of infections is likely to be significantly higher than those reported.
President Andrés Manuel López Obrador is eager to restart the country's flagging economy. His government announced a phased plan to lift restrictions in May.
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