Navy Lieutenant-Commander Brook DeWalt, a Guantanamo spokesman, said: "I can tell you that detainees are allowed weekly phone calls, detainees provide their family names and phone numbers.
"If a prisoner called someone not a relative, that would be in violation of policy."
The call is believed to be the first made from Guantanamo Bay to a media organisation by an inmate.
Al-Qurani said he ended up with a broken tooth after one incident of tear-gassing and beating.
Dewalt said the authorities at Guantanamo had no evidence to support al-Qurani's claims.
In January a US judge ordered the release of al-Qurani, who was only 15-years old when he was captured in Pakistan in 2001, after saying there was no evidence to justify his detention.
He is currently in a separate camp in Guantanamo called Camp Iguana, where prisoners go after they have been approved for release before being transferred.
Cory Crider, a member of al-Qurani's legal team, told Al Jazeera on Wednesday it was hard to ascertain how al-Qurani had been treated in recent months as the situation varied from camp to camp within the facility and also there had been "ramping up" of secrecy in the new administration.
However, Crider said the last time she saw al-Qurani before his transfer to Camp Iguana she had seen abrasions on his hands "that I don't really think he did himself".
"I think that where he is now is a significant, significant improvement over where he was before but there's no question ... that over the years this kid has been seriously mistreated," she said.
The allegations by al-Qurani come after claims by several other Guantanamo inmates that they had been subjected to mistreatment, in violation of international law.
Richard Armitage, who served as the US deputy secretary of state during the Bush administration, told Al Jazeera that he could have stepped down in light of Washington's move to act outside the Geneva Convention.
|Barack Obama pledged to end abuse
at Guantanamo Bay [AFP]
"In hindsight, maybe I should have [resigned]," Armitage told Al Jazeera's Avi Lewis.
"But you are in one of those positions where there are many more battles that you have. You maybe fool yourself - you say 'Well, how much worse would X, Y or Z be if I were not here?'"
But Armitage also criticised the US congress for failing to ensure the safety and well-being of Guantanamo detainees.
"You might go back to what was envisioned by the frameworks of the constitution, and that is called congressional oversight," he said.
"This is their [congress'] job. I don't think members of the senate particularly want to look into these things as they may have to look at themselves in the mirror."
Chad to complain
In a related development, the ambassador of Chad to the US told Al Jazeera on Tuesday he would raise the claims of abuse of one of its citizens with the US authorities.
"I will bring these allegations to my authorities and also will talk to my counterparts at the state department," Mahmoud al-Bashir said.
Al-Bashir said he would raise the case with the Office of War Crimes, which advises Hillary Clinton, the US secretary of state, on international and domestic war-crimes issues.
The envoy also said al-Qurani was subjected to mistreatment when he was detained in Pakistan in 2001.
"When he was detained he was only 15 years old. He was not treated as underage. He was treated in isolation. He was subjected to ill-treatment. And we have been working closely with the state department to solve it," he said.
Al-Bashir also said that he had been told that al-Qurani had been set to be released earlier this month and that the Chadian government had assured the US he would be treated fairly on his return.
Al-Qurani said in a phone call to Al Jazeera that the alleged ill-treatment "started about 20 days" before Barack Obama became US president and "since then I've been subjected to it almost every day".
|More than 200 prisoners are still held at the
Guantanamo prison camp [GALLO/GETTY]
On his second day in office, Obama ordered the closure of the prison, which has been heavily criticised by rights groups over reports of ill-treatment of detainees.
He also ordered that prisoners held there be treated in line with the Geneva Conventions, which prohibit the abuse of detainees.
Khaled al-Anisi, a member of the International Committee for the Defence of Guantanamo Detainees, told Al Jazeera he was surprised that inmates of the prison camp were alleging poor treatment during Obama's presidency.
Speaking from the Yemeni capital, Sanaa, on Thursday, al-Anisi said: "We thought the situation would be better in Guantanamo after Obama came to the White House and his order to stop torture there.
"We have discovered the situation has become [worse] than before. People have been behaving badly towards the detainees, more than they did in the Bush administration."