MEXICO CITY — The gruesome murders this month of a woman and a girl in Mexico have shocked the nation, triggering a groundswell of outrage punctuated by near-daily street protests, unbridled fury on social media and growing demands for incisive government action against gender-based violence.

The woman, Ingrid Escamilla, 25, was stabbed, skinned and disemboweled, and the girl, Fátima Cecilia Aldrighett, 7, was abducted from school, her body later found wrapped in a plastic bag. The outcry over their deaths is forcing a reckoning in a country that has long wrestled with violence against women, analysts and activists say.

It is also amounting to a major leadership test for President Andrés Manuel López Obrador — and critics, who have called his response at turns anemic, insensitive and condescending, say he is falling far short.

Xóchitl Rodríguez, a member of Feminasty, a feminist activist collective, said she has been deeply disappointed by the response of Mr. López Obrador, who campaigned as a transformative figure who would defend marginalized populations.