All but one man remained at large Monday as agencies around the region were alerted, the department said in a news release.
Curry County Sheriff Matt Murray said at a news conference Monday the department was working on a variety of leads. Authorities are searching an Albuquerque home and following up on a lead in Cactus, Texas.
"Please do not approach these individuals because they are considered dangerous," Murray said.
The men were discovered missing at 9:45 p.m. Sunday, when Clovis Police Department officers noticed two people in orange jumpsuits worn by jail inmates running near the jail, Murray said.
The inmates apparently had used handmade instruments to cut the hole in the roof near a skylight, he said.
They gained access to the roof area by climbing pipes in a narrow space behind the wall of a shower unit, Murray told The Associated Press.
"We have a feeling that they have split up and went different ways from finding some of the jumpsuits throughout the city," he said. He declined to answer questions.
Murray said in the interview he's unsure whether any of the men may now have weapons.
"It's unknown at this time," he said. "They are dangerous individuals."
The sheriff's department says among the men are convicted murderer Edward Salas of Clovis and Larry McClendon, who was being held on an open count of murder and aggravated robbery.
Salas was sentenced to life in prison last month for the 2005 shooting of a 10-year-old Clovis boy, who was killed when shots were fired through his bedroom window as he slept.
He was being held at the jail before being transferred to the state Department of Corrections, the news release said.
McClendon of Plainview, Texas, was charged with an open count of murder in March for his role in the January 2007 slaying of a secondhand store owner in Clovis.
One man, Victor Apodaca, was chased and captured by Clovis police officers, Murray said.
About 8 a.m. Monday, a Clovis city employee discovered an orange jail jumpsuit in a dumpster several blocks from the jail, Murray said.
New Mexico State Police Lt. Eric Garcia said motorists were being stopped and questioned on roadblocks on the outskirts of the eastern New Mexico town early Monday.
"If they do see or suspect someone who is one of the escapees, they should immediately call 911," Garcia said.
The other at-large men and the charges against them are: Victor Sotelo, 26, of Portales, aggravated assault; Javier Zapata, 19, of Texico, aggravated assault, shooting at a motor vehicle and child abuse; Raynaldo Enriquez, 19, of Clovis, multiple aggravated burglary, robbery and assault and battery charges; Michael England, 29, of Clovis, tampering with evidence and being a felon in possession of a firearm; Louis Chavez, 18, Albuquerque. The charges against Chavez were not disclosed.
Federal agencies, including the U.S. Marshals, are assisting in the investigation, the sheriff's department said.
This escape is not the first for the detention center.
Last year, the jail changed its procedures and policies after an escape in late 2006 of an inmate who slipped out a door and wasn't missed for two days. The inmate was later captured.
The most recent escape before Sunday occurred July 15 when a female inmate hid behind a food cart and was able to reach the street, the Clovis News Journal reported. The woman was caught seconds later after she was knocked down by a passing vehicle while trying to cross a street.