Mexican officials have ordered police to arrest a U.S. Marine suspected of killing his pregnant colleague and fleeing to Mexico, a U.S. Embassy official said Tuesday. That could lead to his extradition or deportation to the United States.

The Embassy official, who wasn't authorized to give a name, said Mexican officials issued a provisional arrest warrant for Marine Cpl. Cesar Laurean, which means authorities can take him into custody, on Monday at the request of U.S. officials. The order was first reported by CNN.

Mexican authorities have been working with the U.S. for weeks on the assumption that Laurean was likely in Mexico. A cousin told reporters last week that Laurean visited his liquor store outside the western city of Guadalajara in mid-January, but left without saying where he was headed.

Laurean is being sought on an indictment charging first-degree murder of Lance Cpl. Maria Lauterbach, who had accused Laurean of rape. Lauterbach's charred remains were found this month with those of her fetus in a fire pit in Laurean's back yard in Jacksonville, North Carolina. Both were stationed at nearby Camp Lejeune.

Laurean left a note for his wife, Christina, saying Lauterbach slit her own throat and that he buried her in the woods near their home. But an autopsy found that Lauterbach died of blunt force trauma to the head.

For much of the 1980s and 1990s, Mexico was hesitant to extradite foreigners, but U.S. officials have praised increased cooperation in recent years. State Department officials said Mexico extradited 73 suspects to the U.S. in 2007, most to face drug or murder charges.

Sometimes Mexico will forgo the traditional extradition and deport a suspected criminal for entering the country illegally -- a much quicker process. More than 150 U.S. citizens were deported from Mexico last year.

However, Mexico still won't extradite anyone facing the death penalty. U.S. prosecutors haven't said whether they will seek that punishment for Laurean.