A New Mexico official who serves as commissioner of a county near the U.S.-Mexico border said Sunday the state's Democratic governor has not responded to a request to redeploy National Guard troops and that he is moving to block migrants from being released in his county because of a lack of resources.

Couy Griffin, the chairman of the Otero County Commission, said Gov. Michelle Lujan Grisham's office has been silent since the board voted April 18 to declare a state of emergency.

"We've had no response from our governor," Griffin said in a Fox News interview Sunday morning.

Former Republican Gov. Susana Martinez said the southern region of the state is running out of room in local communities to take in tens of thousands of migrants who are being released from federal custody each month. "There is no more capacity any more they're giving to the local community — Las Cruces, Otero county giving it to Yuma, here in El Paso. At one point, they have to bus them to other locations that can absorb them. It just is impossible," Martinez said.

Griffin vowed to "push very hard" against migrants being relocated and released in Otero County, which is home to about 65,000 people. He said the commission is planning to vote on a resolution that would block people who illegally crossed from Mexico to the United States from being bused from El Paso to his county.

"The hypocrisy in what is going on today ... is Santa Fe, which declares to be a sanctuary county, their mayor recently said, 'We don't want them here.' They are not going to receive them in Santa Fe county, but yet they will raise the funds so you all can put them in your backyard. My position, if you'll declare yourself a sanctuary county put them on the plaza and let them live there," Griffin said.

Local officials from the state's southeastern county had given the governor one week to take emergency action and said they will consider suing the state if nothing happens in that time. It's been 10 days since they requested help.

The county wants National Guard troops that Gov. Lujan Grisham's Republican predecessor, Susana Martinez, had sent to the region last April to be deployed again. Lujan Grisham pulled the 118 troops as well as those from other states who had been working with Customs and Border Protection on the southern border.

Martinez said Sunday the Guard's assistance had allowed agents to return to the field from administrative duties and other tasks, as well as highway checkpoints that were closed late last month.

The El Paso Border Patrol sector includes all of New Mexico's border and has seen the second-highest number of families arriving at, and illegally crossing, the southern border since October.

From Oct. 1, 2018, through March 31, agents in the El Paso region apprehended 53,000 people who claimed to be traveling with a family member. Only the Rio Grande Valley sector in Texas saw more members of families arrested: 78,000. The other seven sectors along the southwest border saw anywhere from approximately 500 to 25,000 family members.

Earlier this month, Yuma, Ariz., a city on the border, became the first to declare a state of emergency because it lacks the resources to handle the influx of people being apprehended and released from federal custody.