The families of the young men gathered under a white tarp in front of Mexico City's cathedral at the historic Zocalo square and declared the start of their protest yesterday at 7:00 pm local time (0530 IST).
The parents held signs with the pictures and names of their sons, and sat down as a doctor examined them to make sure they could take part in the nearly two-day fast.
"For 43 hours, we will only drink water and will be fasting when we meet with the president," Nardo Flores, whose son Bernardo is among the missing, told AFP.
The Mexican leader and the families will come face-to-face at 1:00 pm in a museum at the city's vast Chapultepec park.
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Vidulfo Rosales, the parents' attorney, said they will call on Pena Nieto to order a new investigation and for authorities to present the 43 young men alive.
The students, from a rural teacher college in the southern state of Guerrero, disappeared after they were attacked by local police in the city of Iguala.
But the official investigation was questioned by independent experts from the Inter-American Commission on Human Rights, who said there was no evidence that the students were burned in a funeral pyre at a garbage dump.