President Enrique Pena Nieto has told the families of 43 students who disappeared a year ago in southern Mexico that he will create a new special prosecutor for all of the country's thousands of missing people.
Eduardo Sanchez, the president's spokesman, told reporters after the closed-door meeting on Thursday that the families had presented eight demands and that Pena Nieto had instructed his cabinet to analyze each and get back to them.
More than 25,000 people have disappeared in Mexico between 2007 and July 31, 2015, according to the government.
The students' disappearance on September 26, 2014, almost one year ago, brought the issue back into the spotlight.
Vidulfo Rosales, a lawyer representing the families, said they "totally reject" the creation of a special prosecutor for all of the country's missing.
He said the case of the 43 missing students requires its own special prosecutor.
Among the families' demands are a new internationally supervised investigation of the disappearances and an investigation of those responsible for the initial inquiry, which the families believe was intended to mislead them.
Sanchez said after the meeting that there was not a clear timeframe for when the demands would be answered, but that it would be done promptly.
"Again and again we ask ourselves how could we trust again in an institution that tricked us," the families wrote in the letter delivered to the president.
Sanchez said Pena Nieto told the families: "We're on the same side. You and I are looking for the same thing."
After the meeting, Mario Gonzalez, whose son is among the missing students, pointed out that what the government once held up as a "historic truth" about the disappearances, it now calls a hypothesis.
"What guarantee do we have that this new investigation won't be more theatre?" Gonzalez said, surrounded by other parents in Mexico City's central plaza. "We're not going to give up; we're going to continue searching."
Pena Nieto did not agree to any of the families' demands and the only commitments he offered were ones they had already heard, Rosales said.
The students, who disappeared in the city of Iguala, had gone there to commandeer buses that they wanted to use to attend a commemoration in Mexico City.
The federal government has said local police from Iguala and the nearby town of Cocula illegally detained the students and turned them over to the local drug gang Guerreros Unidos, which then allegedly killed them and incinerated their remains.
The families have never accepted that version.
The government has said that it has identified two of the students from the burned remains recovered from a river in Cocula.
A team of international experts sent by the Inter-American Commission on Human Rights, which spent six months reviewing the government's investigation, found a number of shortcomings and points of concern.
Specifically, it concluded the bodies of 43 students could not have been burned at the rubbish dump in Cocula as the government maintained.
Attorney General Arely Gomez earlier said that portion of the government's investigation would be reviewed with assistance from top international experts.
Sanchez confirmed on Thursday that international experts would be involved in a third investigation of the alleged incineration site.