Saudi Arabians Mani Shaman Turki al-Habardi Al-Utaybi and Yassar Talal Al-Zahrani and Ali Abdullah Ahmed, were the prisoners who hanged themselves, the department said in a statement released to The Associated Press.
Ahmed's nationality was not provided, but U.S. military officials earlier said that two Saudis and one Yemeni had taken their lives. The two Saudis had been identified earlier by Saudi officials.
U.S. authorities allege Ahmed was a mid- to high-level al Qaeda operative. Al-Zahrani was accused of being a Taliban front-line fighter who bought weapons for offensives against the United States.
Al-Utaybi was recommended for transfer to the custody of another country before his suicide, the Defense Department said.
The three committed suicide early Saturday morning and were the first reported deaths at the detention center for suspected terrorists.
"They hung themselves with fabricated nooses made out of clothes and bedsheets," Navy Rear Adm. Harry Harris told reporters in a conference call on Saturday.
Harris described the suicides as an "act of asymetric warfare" and not one of deperation. He said the three deaths appeared to be a coordinated effort.
The men were found "unresponsive and not breathing in their cells," according to a statement from the Miami-based command with jurisdiction over the prison. Attempts were made to revive the prisoners, but they failed.
President Bush, spending the weekend at Camp David, was notified of the incident. Mr. Bush's spokesman said the president "expressed srious concern" about the suicides.
The State Department was consulting with the governments of the home countries of the three prisoners, whose names were not being released.
The military said in its statement that "all lifesaving measures had been exhausted" in the attempt to revive the detainees. The remains were being treated "with the utmost respect," an issue important to Muslims. A cultural adviser was assisting the military.
The Naval Criminal Investigative Service is investigating the deaths.
The United States is holding about 460 men on suspicion of links to al Qaeda and the Taliban at Guantanamo Bay, which has become a sore subject between President 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," Mr. 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.
"But while the process drags on," said CBS News foreign affairs analyst Pamela Falk, "the detention facility has been criticized by international organizations as well as U.S. allies, with the British Attorney General adding his voice to the chorus last month."
"Splitting hairs on what is or is not international law misses the point: the protests and suicide attempts reflect the desperation of detainees who may or may not be guilty of terrorism," adds Falk. "The main criticism is that prisoners should be tried and either convicted or released, including those taken on the battlefield."
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.