CIA officers revealed a clash over how quickly they should go help the besieged US ambassador during the September 2012 attack on an outpost in Benghazi, in Libya, and a standing order for them to avoid violent encounters, according to a congressman and others who heard their private congressional testimony or were briefed on it.

The Obama administration has been dogged by complaints that the White House, Pentagon and State Department may not have done enough before and during the attack to save US ambassador Chris Stevens and three other Americans who died, and by accusations that it later engaged in a cover-up.

One allegation was that US officials told the CIA to "stand down" and not go to the aid of the Americans. Top CIA and Defense and State Department officials have denied that. The testimony from the CIA officers and contractors who were in Libya on the night of 11 September 2012 bolsters those denials, but also sheds light on what may have led to the delay of up to 30 minutes to respond, according to the varying accounts.

None of those who testified said a quicker response would have saved the lives of Stevens and the communications specialist Sean Smith at the temporary diplomatic facility in Benghazi.

The senior CIA officers in charge in Libya that day told Congress of a chaotic scramble to aid Stevens and others who were in the outpost when it was attacked by militants on the 11th anniversary of the terrorist attacks of 11 September 2001. Those CIA leaders decided they and their security contractor team should wait before rushing from their annex into the violence roughly a mile away. They said they were trying to first gather intelligence and round up Libyan militia allies armed with heavy weapons, according to the testimony by the CIA officers in charge. Some CIA security contractors disagreed with their bosses and wanted to move more quickly.

Republican Representative Lynn Westmoreland, who leads a House intelligence subcommittee that interviewed the employees, said he believes this disagreement was the source of allegations that the CIA ordered security personnel to "stand down" and not help the people inside the diplomatic mission, and perhaps was the source of accusations that the administration failed to answer a call from the CIA security team for combat aircraft.

"The team leader knew he was on his own," said Westmoreland. He explained that the lack of air support was clear to all CIA employees working in Libya because of a 2011 CIA memorandum sent to employees after Nato forces ended their mission in support of the Libyan revolution.

"It basically told people in Benghazi … if you are attacked, you get your 'package' [the personnel they are charged with protecting] and you get out," Westmoreland said in an interview with the Associated Press.

A senior intelligence official confirmed that the CIA officers on the ground in Benghazi responded to the diplomats' call for help by trying "to rally local support for the rescue effort and secure heavier weapons". When it became "clear that this additional support could not be rapidly obtained", the team moved toward the diplomatic compound.

The official spoke on condition of anonymity because he was not authorized to discuss the attack publicly by name.

One contractor testified that he shouted repeatedly over the agency's radio system to his CIA security boss that they should request combat aircraft. But the security chief explained to lawmakers that he ignored his subordinate's demands because he said he knew that no combat aircraft were available for such a mission, Westmoreland said.

Westmoreland said the CIA security contractors loaded into two vehicles, with weapons ready, the moment they heard the radio call for help from the diplomatic building. Some wanted to rush to the US compound, and their agitation grew as they heard increasing panic when the diplomats reported the militants were setting the compound on fire.

The CIA team leader and the CIA chief at the Benghazi annex told committee members that they were trying to gather Libyan allies and intelligence before racing into the fray, worried that they might be sending their security team into an ambush with little or no backup.

At least one of those security contractors, a former US army ranger, was told to "wait" at least twice, and he argued with his security team leader, according to his testimony that was related by Westmoreland. Westmoreland declined to share the names of the officers who testified because they are still CIA employees.

According to previous accounts by US officials, the attacks began at approximately 9.40pm, and the CIA team arrived roughly 25 minutes into the attack.

None of those who testified would say they believed the ambassador or the others could have been saved had they arrived any faster, according to two officials, who also were briefed on the testimony. They spoke on condition of anonymity because they were not authorized to discuss the closed testimony publicly.

When the seven CIA employees reached the diplomatic compound, they fought their way in and found the five State Department security personnel who had taken shelter in various parts of the compound.

They found computer specialist Smith, dead from smoke inhalation, but couldn't find Stevens and decided to fall back to the CIA annex, because the crowd was building outside again, Westmoreland and the other officials said. Stevens was found in a safe room and taken by Libyan civilians to a nearby hospital, but he died from smoke inhalation.

The CIA team believes their convoy was followed back to their compound, where they were first attacked by small-arms fire around midnight local time, which quickly stopped when the CIA team returned fire, Westmoreland said. Roughly five hours later, the CIA team testified that mortars hit, killing former navy Seal Tyrone Woods, who had helped rescue the diplomats, and former Seal Glenn Doherty, who had just arrived with a team from Tripoli.