Ms Morales said 17 suspects tied to the brutal Zetas drug gang have been detained in relation to the killings in the northern state of Tamaulipas.
Some members of the gang have already confessed to abducting passengers from buses and killing them.
President Felipe Calderon said one 19-year-old man had confessed to killing more than 200 people.
Interior Secretary Francisco Blake Mora pledged to step up the presence of troops and police in the area where the killings occurred. He also said he would not leave the area until the killers and drug gang members there have been caught.
“Organised crime, in its desperation, resorts to committing atrocities that we can’t and shouldn’t tolerate as a government and as a society,” Mr Blake said.
The graves were found earlier this month in the township of San Fernando, the same area of Tamaulipas where investigators found the bodies of 72 migrants, travelling through the area in an effort to reach the US, massacred by suspected drug cartel gunmen last August.
Police say witnesses in the latest killing case have told them that gunmen pulled the victims, mostly young men, off passenger buses travelling through the San Fernando area in late March.
Authorities blame the abductions on the Zetas gang, the same group accused in the migrant killings.
The motive for the bus abductions remains unclear, though prosecutors have suggested the gang may have been forcefully recruiting people to work for it.
San Fernando is a town about 145 kilometres south of Brownsville, Texas, on a well-travelled stretch of highway that runs near the Gulf Coast. It is an area regularly patrolled by the Mexican military.
The Zetas and rival Gulf Cartel are fighting in Tamaulipas over lucrative drug transit routes to the US.
Authorities are working to identify the bodies through DNA samples and other techniques.
One of the bodies discovered is that of a Guatemalan man, the government of that Central American nation said.
The Guatemalan foreign ministry revealed that the victim was Feliciano Tagual Ovalle, 44. However, the ministry did not say whether the man was a migrant passing through or a resident of Mexico.
It said the Guatemalan government planned to bring the body home.
The Zetas drug gang is headed by Heriberto “The Executioner” Lazcano, who is said to have a huge arsenal of grenades, automatic weapons and rocket launchers.
Mexican officials say the Zetas could have as many as 10,000 members across Mexico, Central America and the US, more than any other Mexican cartel. It is also believed that the gang is currently in the middle of an aggressive expansion drive.