In a statement on Friday, the spokesman also said that inmates clashed with guards trying to stop a prisoner hanging himself.
The three other inmates took overdoses in attempting suicide.
Robert Durand, a spokesman for Joint Task Force (JTF) Guantanamo, which runs the camp in Cuba, said on Friday that all four were being treated and their lives were not in danger.
Durand said in a statement that JTF guards had responded to a disturbance in a medium-security part of the camp late on Thursday. "A detainee in Camp 4 was preparing to hang himself," he said.
He said that when the guard force entered the compound to intervene, some inmates "attempted to prevent them from rescuing the detainee by using fans, light fixtures and other items as improvised weapons. Minimum force was used to quell the disturbance and prevent the suicide".
The statement also said that, earlier in the day, "three detainees ingested prescription medications that apparently had been hoarded for this purpose".
JTF Guantanamo did not identify the inmates nor give reasons for the suicide attempts.
According to lawyers who have visited the camp, there is widespread depression among the 460 or so inmates, most of whom have been held for more than four years without charge.
The camp was opened in early 2002 to house "enemy combatants" caught in Afghanistan and elsewhere after the "war on terror" was declared in response to the attacks of September 11, 2001.
According to camp authorities, there have been 41 suicide attempts by 23 prisoners since the facility was opened.