Bloodied, wearing just a pair of khaki trousers, and dumped on a cheap mattress, Muammar Gaddafi's body has become a gruesome tourist attraction and a macabre symbol of the new Libya's problems.

Hundreds of ordinary Libyans queued up outside a refrigerated meat store in Misrata, where the dead dictator was being stored as a trophy. A guard allowed small groups into the room to celebrate next to Gaddafi's body. They posed for photos, flashing victory signs, and burst into jubilant cries of "God is great."

Wounds on Gaddafi's body appeared to confirm that he was indeed killed in cold blood in the chaotic minutes following his capture on Thursday. He was found in the town of Sirte, hiding in a drainage pipe. There was a close-range bullet wound on the left side of his head. Blood stains showed another bullet wound to his thorax. His body, subsequently driven to Misrata and publicly paraded, was barefoot and stripped to the waist.

Late on Friday the Gaddafi clan demanded a chance to bury the body. In a statement on a Syria-based pro-Gaddafi television station, the ousted dictator's family asked for the bodies of Gaddafi, his son Mo'tassim and others who were killed on Thursday by fighters who overran his hometown Sirte.

"We call on the UN, the Organisation of the Islamic Conference and Amnesty International to force the [National] Transitional Council to hand over the martyrs' bodies to our tribe in Sirte and to allow them to perform their burial ceremony in accordance with Islamic customs and rules," the statement said.

What to do with the fallen dictator's corpse is the subject of a row inside the National Transitional Council (NTC). Libya's interim prime minister, Mahmoud Jibril, arrived in Misrata to talk with local NTC representatives. They have made it abundantly clear they do not want Gaddafi to be buried in their town. The NTC leadership in Tripoli wants a solution quickly. One popular option is to bury him at sea, like Osama bin Laden.

The dispute threatens to overshadow NTC plans to declare a formal end to Libya's nine-month uprising . The council will announce from Benghazi, where the Libyan revolution began in February, that the project of national liberation is now complete. It will say a new, democratic post-Gaddafi era has begun.

Among ordinary Libyans, there were few regrets about the bloody and preemptive manner of Gaddafi's demise. Most worshippers at Friday prayers in the capital's Martyrs Square said they were pleased Gaddafi had been killed. But one young woman said: "Some people do care about the rule of law and don't think it's right that he should have been assassinated."

The NTC faces questions from international rights organisations. On Thursday, Jibril claimed that Gaddafi had been killed from a bullet to the head received in crossfire between rebel fighters and his supporters. He was dragged alive on to a truck, but died "when the car was moving", Jibril said, citing forensic reports.

Gruesome mobile phone footage obtained by the Global Post undermines this account. It records the minutes after Gaddafi's capture, when his convoy came under Nato and rebel attack. He is dragged out of a tunnel where he had been hiding. Blood is already pouring out of a wound on the left side of his head.

A group of fighters then frogmarch him towards a pick-up truck. There are shouts of "God is great" and the rattle of gunfire. At one point Gaddafi keels over; a fighter kicks him and scuffs dirt over his bloodstained clothing. The rebels prop Gaddafi back on his feet and propel him onwards.

Gaddafi is clearly dazed and wounded – but is alive, conscious, and pleading feebly with his captors. Fighters at the scene said that he was injured in the shoulder and leg when he was found. Fresh blood is also flowing from a head injury.

The evidence has prompted Amnesty International to call on the NTC to investigate. It said that if Gaddafi were deliberately killed, this would be a war crime. The NTC's position is that it will support an investigation because the new Libya is a law-abiding country, but officials seemed sceptical that it was necessary. "Even if he was killed intentionally, I think he deserves this," Mohammed Sayeh, a senior official, told the BBC. "If they kill him 1,000 times, I think it will not pay back the Libyans what he has done."

Amnesty also called for an investigation into the unexplained, violent death of Gaddafi's son Mutassim. Video footage that surfaced shows him calmly smoking a cigarette after his capture. Soon afterwards, someone appears to have shot him. His body is now on show in another freezer unit in Misrata.

In a televised interview, Gaddafi's cousin and former bodyguard claimed it was Mutassim, and not the dictator himself, who had been co-ordinating the loyalist resistance inside Sirte. Mansour Dao, who was captured with Gaddafi, also cast doubt on the account of Nato air strikes against the dictator's convoy. Instead, he said Gaddafi's convoy had received "heavy, heavy gunfire" from pursuing rebels. "They had us circled," he said.

Gaddafi's cousin added that their convoy was not escaping from Sirte, as has been reported, but was heading for the village where Gaddafi was born in the nearby Jarif valley. "Gaddafi did not run away, and he did not want to escape," Dao said. "We left the area [we were staying] towards Jarif, where he comes from. The rebels surrounded all the neighbourhood.

"They launched heavy raids on us which led to the destruction of the cars and the death of many individuals who were with us. After that, we came out of the cars and split into several groups and we walked on foot, and I was with Gaddafi's group that includes Abu Bakr Yunis and his sons and several volunteers and soldiers. I do not know what happened in the final moments, because I was unconscious after I was hit on my back."

One of the rebels who apparently captured Gaddafi told how his brigade had been on its way to support the Tiger Brigade when they spotted a group of "around 15" Gaddafi loyalists, some running right and left. They arrested them. "At that time, we were standing on top of the hole where Gaddafi was hiding," he said.

The unnamed rebel added: "We saw another two people hiding and fired on them ... Our colleague went down and he killed two of them ... Later on, we went to the other side and four or five ran out from under the road. And they surrendered themselves and they told us Gaddafi is hiding inside and is injured.

"When we entered the hole, I saw his bushy head, and I captured him immediately. Then all the fighters came and surrounded him."

The fighters retrieved Gaddafi's golden handgun, together with a second gun and a Thuraya phone.

Nato's role in Gaddafi's death remains controversial. French warplanes and a US Predator drone were involved in the attack on the dictator's convoy.

Russia's foreign minister, Sergei Lavrov, criticised the bombardment. The Kremlin has long complained that it was tricked into not vetoing the security council resolution allowing Nato to enforce a no-fly zone. Lavrov said: "There is no link between a no-fly zone and ground targets, including this convoy. Even more so since civilian life was not in danger because it [the convoy] was not attacking anyone."

The fate of Gadhafi's one-time heir apparent Seif al-Islam, meanwhile, was unclear. Justice minister Mohammed al-Alagi said al-Islam was wounded and being held in a hospital in the city of Zlitan. But information minister Mahmoud Shammam on Friday that the son's whereabouts were uncertain.