Mexican activists have asked the International Criminal Court to investigate President Felipe Calderon over the torture and killing of civilians in the war on drugs.
A petition signed by more than 18,000 people also asks the ICC to investigate Mexico's most-wanted drugs lord, Joaquin "El Chapo" Guzman.
The Mexican government has denied the accusations of crimes against humanity.
It says its security policy cannot constitute an international crime.
Human rights lawyer Netzai Sandoval filed a complaint with the ICC in the Hague, asking it to investigate the deaths of hundreds of civilians at the hands of the security forces and drugs gangs, as well as alleged torture and rape.
"The violence in Mexico is bigger than the violence in Afghanistan, and bigger than the violence in Colombia," Mr Sandoval told Reuters news agency.
"We want the prosecutor to tell us if war crimes and crimes against humanity have been committed in Mexico, and if the president and other top officials are responsible".
The office of the prosecutor said it had received the request and would study it and make a decision in due course.
Rule of law
The Mexican government responded to the complaint when the petition was launched in October.
"The federal government categorically rejects that security policy could be considered an international crime," the foreign ministry said in a statement.
"In our country society is not victim of an authoritarian government or of systematic abuses by the armed forces," it added.
"Mexico has a rule of law under which crime and impunity are fought without exceptions".
The government also stressed its commitment to human rights and responsibility to protect its citizens from criminal violence.
Mexico is a signatory to the 2002 Statute of Rome that established the ICC as the world's first permanent international war crimes court.
The ICC investigates and tries cases of war crimes and crimes against humanity in countries that are unwilling or unable to prosecute them on their own.
Most of its cases are initiated after referral by the country involved or the UN Security Council, but the prosecutor's office can also start investigations on its own initiative on the basis of information received from individuals or organisations.
So far, all its cases have been in Africa, but the prosecutor's office has begun preliminary examinations in other countries including Afghanistan, Colombia, Honduras and Korea.
Correspondents say any decision to begin an investigation into alleged crimes in Mexico could take months or even years to reach.
More than 40,000 Mexicans have died in drug-related violence since December 2006, when President Calderon began using the military to combat the drug cartels.
Many of the dead are thought to be members of the gangs, killed by the security forces or in clashes with rival groups, but there have also been a growing number of civilian casualties.
Last month a report by Human Rights Watch found evidence that the Mexican police and military were involved in 24 killings and 39 disappearances in five states, as well as systematic torture.
It said few of the cases it documented were properly investigated, in part because Mexican soldiers are subject only to military courts.