Texas Gov. Greg Abbott threatened to cut funding for one county after its sheriff announced the agency would be scaling back its cooperation with federal immigration.

Travis County Sheriff Sally Hernandez announced last week she’s scaling back the amount of aid her department provides federal immigration agents in detaining suspects who might be in the country illegally, according to the Austin American-Statesman.

Starting Feb. 1, sheriff’s officials will begin honoring so-called immigration holds or “detainers” placed by federal authorities only when a suspect is booked into the Travis County Jail on charges of capital murder, aggravated sexual assault and “continuous smuggling of persons.”

Otherwise, federal agents must have a court order or arrest warrant signed by a judge for the jail to continue housing a person whose immigration status is in question.

"The public must be confident that local law enforcement is focused on local public safety, not on federal immigration enforcement. Our jail cannot be perceived as a holding tank for ICE or that Travis County deputies are ICE officers," Hernandez said.

Hernandez's announcement came as Texas Republicans are gearing up for a new fight to ban so-called sanctuary cities in the current legislative session.

Abbott responded to the announcement, tweeting his office “will cut funding for Travis County adopting sanctuary policies.”

"Stiffer penalties coming," Abbott's tweet said.

Abbott has pushed the issue to the front of his unofficial agenda for 2017, pledging in interviews and on social media to sign into law a "ban" on cities and local governments that are seen as protecting people in the U.S. illegally, with sanctions such as cutting state funding. Civil rights groups say the threat from the governor could lead to racial profiling.

Travis County could lose up to $1.8 million in grants because the governor's office requires compliance in order to receive grants.

The Travis County sheriff's office has a $169 million budget, according to the county's budget website. The $1.8 million would represent 1 percent of that budget.

"The public must be confident that local law enforcement is focused on local public safety, not on federal immigration enforcement," Hernandez said in a video announcement.

The Associated Press contributed to this report.