The US state department refused to comment on the claims, made to Al Jazeera in a phone call made by al-Qurani from the camp.
Al-Qurani said during the call 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".
Al Jazeera's Monica Villamizar said that the authorities at Guantanamo Bay confirmed to her that al-Qurani would be punished for making the call but did not say how.
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.
|Obama pledged to end abuse at the Guantanamo Bay prison camp [Reuters]
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.
Obama also signed an order ending the harsh interrogation of prisoners - including the waterboarding technique that causes detainees to feel like they are drowning.
The prison camp was set up by the Bush administration in 2002 to hold prisoners it detained as part of its so-called war on terror.
Several hundred detainees have since been released but more than 240 prisoners remain there, including Khalid Sheikh Mohammed, who is suspected of planning the September 11, 2001, attacks on the US.
Describing a specific incident, which took place after the change in the US administration, al-Qurani said he had refused to leave his cell because they were "not granting me my rights", such as being able to walk around, interact with other inmates and have "normal food".
A group of six soldiers wearing protective gear and helmets entered his cell, accompanied by one soldier carrying a camera and one with tear gas, he said.
"They had a thick rubber or plastic baton they beat me with. They emptied out about two canisters of tear gas on me," he told Al Jazeera.
"After I stopped talking, and tears were flowing from my eyes, I could hardly see or breathe.
"They then beat me again to the ground, one of them held my head and beat it against the ground. I started screaming to his senior 'see what he's doing, see what he's doing' [but] his senior started laughing and said 'he's doing his job'.
"He broke one of my front teeth. Of course they didn't film the blood, they filmed my back so it doesn't show."
Al Jazeera provided detailed information of al-Qurani's mistreatment claim to the Pentagon and the US justice department but only received a reply from DeWalt, the Guantanamo spokesman.
"I have no record of authenticity of this," he told Al Jazeera, referring to al-Qurani's accusations.
"It is an alleged phone transcript... We don't have any evidence supporting or substantiating any of these claims."