Texas Goveror Greg Abbott has tweeted that all hostages are safe after a lone gunman kept police at bay for six hours during a standoff inside a Dallas-area synagogue.

“Prayers answered. All hostages are out alive and safe,” Mr Abbott tweeted Saturday night.

Abbott’s tweet came not long after a loud bang and what sounded like gunfire coming from inside the synagogue.

Full details of the rescue operation were not immediately clear, including whether the gunman survived the encounter with SWAT team rescuers.

The man, who has not been formally identified, took hostages on Saturday (local time) during services at the Congregation Beth Israel synagogue where he could be 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.

At least four hostages were initially believed to be inside the synagogue, according to three law enforcement officials.

The synagogue’s rabbi was believed to be among the hostages.

FBI Special Agent in Charge Matt DeSarno later said the hostage-taker was killed and a team would investigate “the shooting incident”.

Agent DeSarno said the hostage-taker was specifically focused on an issue not directly connected to the Jewish community, and there was no immediate indication that the man was part of any broader plan.

But he said the agency’s investigation “will have global reach”.

The Colleyville Police Department said the first hostage was released uninjured shortly after 5pm Saturday and did not require medical attention.

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-Qaeda, the officials said.

The gunman, who described Siddiqui as “my sister”,  demanded to be allowed to speak with her, according to the officials. Siddiqui is in federal prison in Texas.

Police were first called to the synagogue around 11am, immediately ordering the evacuation of nearby residents.

The services were being livestreamed on the synagogue’s Facebook page and captured audio of the man saying, “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.

The Fort Worth Star-Telegram reported that “an angry man” could be heard ranting and talking about religion before Facebook took down the feed.

While he hostage-taker clearly referred to Siddiqui as his “sister”, Faizan Syed, executive director of Council on American-Islamic Relations in Dallas Fort-Worth Texas, told The Associated Press that Siddiqui’s biological brother, Mohammad Siddiqui, was not involved.

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.

“This latest antisemitic attack at a house of worship is an unacceptable act of evil,” CAIR National Deputy Director Edward Ahmed Mitchell said in a statement. “We stand in solidarity with the Jewish community, and we pray that law enforcement authorities are able to swiftly and safely free the hostages. No cause can justify or excuse this crime.”