The divisional court rejects the emergency legal request for a ban on abortions, since 1973.
The Supreme Court of the United States has refused to overturn Texas law banning abortions six weeks after pregnancy.
Judges voted 5-4 on Thursday morning to reject the emergency request from abortionists and others seeking to block the implementation of the law.
The so-called Heartbeat Act, which went into effect Wednesday, represents a complete ban on abortion in Texas.
Signed by Republican ambassador Greg Abbott in May, the law prohibits abortion when medical professionals can detect cardiac events, especially about six weeks before most women find out they are pregnant.
Proponents of abortion claim that such bans have been outlawed since the Supreme Court ruled in Roe v Wade, a landmark ruling that allowed abortion nationwide in 1973.
The Supreme Court has ruled that its ruling provides no provision for Texas law and allows legal complications to be enforced.
“By the end of the process, we are confident that we are not talking about eliminating any cases or cases that they may request,” many said at the site.
“In particular, this law is not based on any of the provisions of Texas law, and does not prohibit any other activities in violation of Texas law, including Texas state courts.”
Chief Justice John Roberts, Justice Stephen Breyer, Justice Sonia Sotomayor and Justice Elena Kagan all denied the allegations.
Sotomayor said the majority vote was “surprising”.
“By calling for the enactment of an illegal law to ban women from exercising their legal rights and avoiding criminal prosecution, many judges have decided to bury their heads in the sand,” she said in a statement.
U.S. President Joe Biden called the law “dangerous” and said it was “a clear violation of a law enacted under the leadership of Roe v Wade and kept as a model for almost half a century”.
“My supervisors are deeply committed to the laws governing Roe v Wade almost 50 years ago and will protect and defend this right,” he said in a statement.
Julia Kaye, lawyer for the American Civil Liberties Union’s Reproductive Freedom Project, told Al Jazeera that there was “corruption and chaos” in Texas because of the law.
“There are thousands of pregnant Texans sitting at their desk in the kitchen trying to reduce the numbers and see how they can travel long distances from the government, to receive timely medical treatment,” he said.
Areas of racial and ethnic minority Texans may be particularly affected by the law, he said.