They are the first deaths reported at the detention center in Cuba, where the United States is holding about 460 men on suspicion of links to al Qaeda and the Taliban.
It was not immediately clear when the inmates died.
It also was not clear whether the suicides were connected to a violent clash last month between detainees and military guards at Guantanamo.
The Pentagon scheduled a briefing for later Saturday.
President Bush, spending the weekend at Camp David, was notified of the incident, said the official, who spoke on condition of anonymity because the Pentagon was announcing the details.
There also is a hunger strike among detainees, though the number of inmates refusing food dropped to 18 by last weekend from a high of 131.
The prison is a sore subject between Mr. Bush and U.S. allies who otherwise are staunch supporters of his policies.
A U.N. panel said May 19 that holding detainees indefinitely at Guantanamo violated the world's ban on torture. The panel said the United States should close the detention center.
German Chancellor Angela Merkel, Danish Prime Minister Anders Fogh Rasmussen and British Attorney General Lord Goldsmith are among those who also recently have urged the United States to close the prison.
On Friday, after the prison came up during a meeting with Fogh Rasmussen at Camp David, Mr. Bush said his goal is to do just that.
"We would like to end the Guantanamo, we'd like it to be empty," Bush said. But he added: "There are some that, if put out on the streets, would create grave harm to American citizens and other citizens of the world. And, therefore, I believe they ought to be tried in courts here in the United States."
Mr. Bush said his administration was waiting for the Supreme Court to rule whether he overstepped his authority in ordering the detainees to be tried by U.S. military tribunals. "We're waiting on our Supreme Court to act," he said.
There have been increasing displays of defiance from Guantanamo Bay prisoners, who have been held for up to 4 1/2 years with many claiming their innocence.
Until now, Guantanamo officials have said there have been 41 suicide attempts by 25 detainees and no deaths since the United States began taking prisoners to the base in January 2002. Defense lawyers contend the number of suicide attempts is higher.
On May 18, in one of the prison's most violent incidents, a detainee staged a suicide attempt to lure guards into a cellblock where they were attacked by prisoners armed with makeshift weapons, the military said. Earlier that day, two detainees overdosed on antidepressants they collected from other detainees and hoarded in their cells. The men have since recovered.
There also has been a hunger strike among detainees since August. The number of inmates refusing food dropped to 18 by last weekend from a high of 131. The military has at times used aggressive force-feeding methods, including a restraint chair. Force-feeding is performed through tubes inserted into the nose.
Physicians for Human Rights has called on the United States to halt the "brutal and inhumane force-feeding tactics." U.S. officials have said the measures are "safe and humane" and have been used in American civilian prisons.