Authorities have confirmed all hostages are safe and a hostage-taker is dead after a stand-off inside a Dallas-area synagogue.

The man had taken four hostages during Saturday services at the Congregation Beth Israel synagogue where he was heard ranting in a livestream and demanding the release of a Pakistani neuroscientist who was convicted of trying to kill US army officers in Afghanistan.

Texas's Governor Greg Abbott tweeted the group were safe not long after a loud bang and what sounded like gunfire was heard coming from the synagogue.

One hostage was released during the stand-off, and three others were rescued when authorities entered the building.

Authorities are not saying how the hostage-taker was killed, but one law enforcement official had said earlier today that he was armed. 

FBI Special Agent in Charge Matt DeSarno said the man had been identified “but we are not prepared to release his identity or confirm his identity at this time."

He said there was no immediate indication that the man had connections to any broader plan but said the investigation "will have global reach."

The FBI also said the man involved was specifically focused on an issue not directly connected to the Jewish community.

In a Facebook livestream 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.

Rant captured on Facebook livestream

Police were first called to the synagogue around 11am , after the synagogue rabbi called another Rabbi in New York City.

People were evacuated from the surrounding neighbourhood soon after that, FBI Dallas spokesperson Katie Chaumont said earlier today.

She said there were no reported injuries.

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.

Mr 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," Ms Francis said.

"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"

"He was clearly in extreme distress."

She said it sounded like the man was talking to the police department on the phone, with the rabbi and another person trying to help with the negotiations.

Anna Salton Eisen, a founder and former president of the synagogue, said the congregation has about 140 members and the rabbi had worked hard to build interfaith relationships in the community.

"This is unlike anything we've ever experienced. You know, it's a small town and it's a small congregation," Ms Eisen said.

"No matter how it turns out, it's hard to fathom how we will all be changed by this, because surely we will be."

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

Neuroscientist accused of shooting US Army officers 

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.