Two families of Syrian refugees are due to arrive in Texas on Monday despite efforts by the state to bar their resettlement, including a lawsuit Texas filed last week in federal court.

A family of six, comprised of the parents, two children under age 6 and the children's grandparents, are scheduled to arrive in Dallas. Another family of six, comprised of four children aged 2 to 13 and their parents, are set to arrive in Houston, the U.S. Justice Department said in a court filing.

The agencies resettling the families did not respond to requests to confirm their arrival. The refugees arrived last week in New York.

The results of the case filed in U.S. District Court in Dallas could determine whether the governors of about 30 states will be able to go through with plans to bar the local resettlement of Syrian refugees.

A federal judge on Monday denied a request by Texas for a hearing by Wednesday for an injunction to bar Syrian refugees from resettling, an activist group said.

"The parties will submit briefings over the course of the next few weeks, after which the judge will take up the request for a preliminary injunction," said Anna Núñez, a spokeswoman with the American Civil Liberties Union of Texas, which has worked on the case.

Following the deadly Paris attacks in November, Texas Governor Greg Abbott, a Republican, was one of the first governors to seek to block the resettlement of Syrians.

Abbott has said he was concerned U.S. security screening is ineffective and could allow people with ties to terrorism to be admitted.

The U.S. Justice Department said Texas did not have the authority to act on immigration policy and could not bar the refugees.

The International Rescue Committee, also a party in the suit, said barring entry to a state based on nationality violates U.S. civil rights laws.

In November, a family of Syrian refugees settled in Connecticut after the Republican governor of Indiana, where the trio had been headed, said he did not want Syrian refugees entering his state.

Texas has been one of the main U.S. relocation sites for Syrians since the country's civil war erupted about four years ago. Since fiscal year 2011, 243 Syrian refugees have resettled in Texas, the U.S. filing said.

Another family of eight Syrians is due to resettle in Houston on Thursday, along with a 26-year-old woman whose mother resides in the area, court filings showed.