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The hostages had been held captive since October in Somalia, but on Tuesday, a U.S. Special Operations team freed them with a swiftness and lethal force reminiscent of the raid on Usama bin Laden's compound in Pakistan.

The raid Tuesday was conducted by a joint team overseen by Africa Command and involved Navy SEAL Team Six, the same unit -- though not the exact same individuals -- that killed bin Laden in May, a senior U.S. military source told Fox News.

President Obama authorized the operation at 9 p.m. Monday. By the time he was about to begin his State of the Union address 24 hours later, the mission was complete. The two hostages, an American and a Dane, were free and nine kidnappers were dead.

American Jessica Buchanan, 32, and Dane Poul Hagan Thisted, 60, had been working with a de-mining unit of the Danish Refugee Council when they were kidnapped in October.

Pentagon spokesman George Little told reporters on Wednesday that the major reason for conducting the operation was due to Buchanan's deteriorating health. U.S. officials tell Fox News they worried that a previous infection was leading to possible kidney failure, a potentially life-threatening, pre-existing medical condition.

Obama authorized the operation after being briefed in the White House residence by his national security adviser. Military commanders finalized the raid on Tuesday. More than 50 U.S. troops were involved.

Officials with knowledge of the mission told Fox News that on the moonless night a rescue team dropped into the area from parachutes off fixed-wing aircraft. From their drop point they hiked to the encampment in a wide open, shrubby area. The hostage takers were not inside any compound, rather they were all out in the open -- many of them sleeping.

The militants fired first and the SEALs quickly responded, killing all nine hostage takers in a matter of seconds. When the hostages were secured everyone left on combat helicopters for Camp Lemonnier in neighboring Djibouti.

The captors were heavily armed and had explosives on them, Little said. There were no known survivors among the kidnappers. No Americans were injured during the raid, he said.

The operation was an interagency effort. The FBI had been monitoring the hostages, using local Somali elders as intermediaries to deliver medicine.

The operation and rescue was confirmed by the president early Wednesday in a statement. He said the operation serves as yet another message to the world that the U.S. "will stand strongly against any threats to our people."

"Jessica Buchanan was selflessly serving her fellow human beings when she was taken hostage by criminals and pirates who showed no regard for her health and well-being," he said. "As commander in chief, I could not be prouder of the troops who carried out this mission, and the dedicated professionals who supported their efforts."

Defense Secretary Leon Panetta also praised the mission early Wednesday, saying the operation was a "team effort" between multiple departments.

"This successful hostage rescue, undertaken in a hostile environment, is a testament to the superb skills of courageous service members who risked their lives to save others," he said.

The president appeared to refer to the mission before his State of the Union address in Washington Tuesday night. As he entered the House chamber in the U.S. Capitol, he pointed at Defense Secretary Leon Panetta in the crowd and said, "Good job tonight."

The White House later announced that following his State of the Union Speech, the president called Jessica's father, John Buchanan, to tell him his daughter was safe.

House Intelligence Committee Chairman Mike Rogers, R-Mich., also praised the special force, and said they and intelligence professionals "yet again showed the reach and determination of our nation to combat terrorism and protect our citizens and our allies."

Panetta visited Camp Lemonnier in Djibouti, where the rescued hostages were taken, just over a month ago. A key U.S. ally in the region, Djibouti has the only U.S. base in sub-Saharan Africa. It hosts the military's Combined Joint Task Force-Horn of Africa.

The Danish Refugee Council said both freed hostages are unharmed. The group said in a separate statement that the two "are on their way to be reunited with their families."

The two aid workers appear to have been kidnapped by criminals -- and not by Somalia's Al Qaeda-linked militant group al-Shabaab. As large ships at sea have increased their defenses against pirate attacks, kidnappers have looked for other money-making opportunities on land.

A kidnapper who gave his name as Bile Hussein said he had spoken to his cohorts at the scene of the raid and they reported that nine captors had been killed. A second kidnapper who gave his name as Ahmed Hashi said two helicopters attacked at about 2 a.m. at the site where the hostages were being held about 12 miles north of the Somali town of Adado.

The Danish Refugee Council had earlier enlisted traditional Somali elders and members of civil society to seek the release of the two hostages. The two were seized in October from the portion of Galkayo town under the control of a government-allied clan militia. The aid agency has said that Somalis held demonstrations demanding the pair's quick release.

Their Somali colleague was detained by police on suspicion of being involved in their kidnapping.

The two hostages were working in northern Somalia for the Danish Demining Group, whose experts have been clearing mines and unexploded ordnance in conflict zones in Africa and the Middle East.

Several hostages are still being held in Somalia, including a British tourist and two Spanish doctors seized from neighboring Kenya, and an American journalist kidnapped on Saturday.

Fox News' Jennifer Griffin and Justin Fishel and The Associated Press contributed to this report.