"Prayers answered. All hostages are out alive and safe," Abbott tweeted on Saturday night.

Abbott's tweet came not long after a loud bang and what sounded like gunfire was heard coming from the synagogue, where authorities said a man had held people captive as he demanded the release of a Pakistani neuroscientist who was convicted of trying to kill US Army officers in Afghanistan.

The hostage-taker was later declared dead, according to a law enforcement official who spoke to The Associated Press on the condition of anonymity. Details of the rescue or the man's death were not immediately released.

At least four hostages were initially believed to be inside the synagogue, according to three law enforcement officials who were not authorised to discuss the ongoing investigation and who spoke to the AP on the condition of anonymity.

The synagogue's rabbi was believed to be among the hostages, one of the officials said. One of the officials said the man claimed to be armed but authorities had not confirmed whether he was.

The Colleyville Police Department said one hostage was released uninjured shortly after 5pm on Saturday. The man was expected to be reunited with his family and did not require medical attention. A law enforcement official said the first hostage who was released was not the rabbi.

Authorities are still trying to discern a precise motive for the attack. The hostage-taker was heard demanding the release of Aafia Siddiqui, the Pakistani neuroscientist suspected of having ties to al-Qaida, the officials said.

He also said he wanted to be able to speak with her, according to the officials. Siddiqui is in federal prison in Texas.

The officials said investigators have not positively identified the man and cautioned that the information was based on a preliminary investigation.

A rabbi in New York City received a call from the rabbi believed to be held hostage in the synagogue to demand Siddiqui's release, a law enforcement official said. The New York rabbi then called 911.

Police were first called to the synagogue around 11am and people were evacuated from the surrounding neighbourhood soon after that, FBI Dallas spokesperson Katie Chaumont said.

The services were being livestreamed on the synagogue's Facebook page for a time. The Fort Worth Star-Telegram reported that an angry man could be heard ranting and talking about religion at times during the livestream, which didn't show what was happening inside the synagogue.

Shortly before 2pm, the man said, "You got to do something. I don't want to see this guy dead." Moments later, the feed cut out. A Meta company spokesperson later confirmed that Facebook removed the video.

Multiple people heard the hostage-taker refer to Siddiqui as his "sister" on the livestream, but Faizan Syed, the executive director of Council on American-Islamic Relations in Dallas Fort-Worth Texas, told The Associated Press that Siddiqui's brother, Mohammad Siddiqui, was not involved.

Syed said CAIR's support and prayers were with the people being held in the synagogue.

Texas resident Victoria Francis told the AP that she watched about an hour of the livestream before it cut out. She said she heard the man rant against America and claim he had a bomb.

"He was just all over the map. He was pretty irritated and the more irritated he got, he'd make more threats, like 'I'm the guy with the bomb. If you make a mistake, this is all on you'. And he'd laugh at that," she said. "He was clearly in extreme distress."

White House press secretary Jen Psaki tweeted Saturday evening that President Joe Biden had been briefed and was receiving updates from senior officials.

Israeli Prime Minister Naftali Bennett said he was monitoring the situation closely. "We pray for the safety of the hostages and rescuers," he wrote on Twitter.

CAIR, the nation's largest Muslim advocacy group, condemned the attack Saturday afternoon.

Siddiqui earned advanced degrees from Brandeis University and the Massachusetts Institute of Technology before she was sentenced in 2010 to 86 years in prison on charges that she assaulted and shot at US Army officers after being detained in Afghanistan two years earlier.

The punishment sparked outrage in Pakistan among political leaders and her supporters, who viewed her as victimised by the American criminal justice system.

In the years since, Pakistan officials have expressed interest publicly in any sort of deal or swap that could result in her release from US custody, and her case has continued to draw attention from supporters.

In 2018, for instance, an Ohio man who prosecutors say planned to fly to Texas and attack the prison where Siddiqui is being held in an attempt to free her was sentenced to 22 years in prison.

Australian Associated Press