MEXICO CITY (REUTERS) - Following criticism from the United Nations, the Mexican Senate has postponed until 2021 a debate on a draft law that would limit the involvement of federal prosecutors in the search for missing people, the Senate media office said on Wednesday (Dec 9).

Many of Mexico's almost 80,000 people registered as missing are victims of gang-related violence, which is on track to fuel a record number of homicides for a third year running in 2020, despite a pledge by President Andres Manuel Lopez Obrador to get a grip on the problem.

The office of the UN High Commissioner for Human Rights this week wrote in a letter, which was seen by Reuters on Wednesday, that Mexico should subject the Bill to more vetting by politicians, families of victims and experts.

The letter was received in the Senate and contributed to the decision to suspend a discussion of the Bill, the media office said.

"They are going to open a broader process of analysis and discussion," a Senate source told Reuters, noting debate on the proposal would be postponed until 2021.

The initiative pushed by Mr Lopez Obrador's ruling party aims to overhaul the law governing the attorney-general's office to streamline its functioning.

Critics argue the law would undermine prosecutors' independence in investigations while reducing their legal responsibility to investigate cases of missing people.

The federal government's own National Search Commission said in a strongly worded statement that the Bill should be scrapped permanently, arguing that it would mark a major step backwards in creating a legal system to prevent people from disappearing.

The commission has registered more than 79,600 missing people, more than 4,000 illicit graves, and tens of thousands of unidentified bodies in morgues.

Only 35 cases against disappearing people, a crime in Mexico, have led to sentencing, the commission says.