The fight between Gov. Sam Brownback of Kansas and the state’s judicial branch has escalated, with the governor last week signing into law a bill that could strip state courts of their funding.

The measure, at the end of a lengthy bill that allocated money for the judiciary this year, stipulates that if a state court strikes down a 2014 law that removed some powers from the State Supreme Court, the judiciary will lose its funding.

The 2014 law took the authority to appoint chief judges for the district courts away from the Supreme Court and gave it to the district courts themselves. It also deprived the state’s highest court of the right to set district court budgets. Critics said the law was an attempt by Mr. Brownback, a Republican, to stack the district courts with judges who may be more favorable to his policies.

The budget bill that Mr. Brownback signed on Thursday was related only to the judiciary. He said he wanted to ensure that the courts would remain open while lawmakers sparred over the larger budget issues. Lawmakers have been debating how to fill a $400 million shortfall, which will most likely require tax increases that Mr. Brownback and many in the conservative-dominated Legislature oppose. If a budget is not passed by Sunday, state workers may be furloughed.