The hostages were freed Tuesday in a gun battle that killed nine captors, Algerian newspapers reported. The clash lasted several hours, with army units trading gunfire with about 10 hostage-takers armed with assault rifles in the desert about 1,200 miles south of Algiers, the Arab-language daily El Watan reported, citing a security official it did not identify.
The report said the Army found the captives using reconnaissance planes equipped with thermal vision gear.
Officials in Germany, Austria and Sweden confirmed the release of 10 Austrians, six Germans and a Swede, who were expected to return home Wednesday. The official news agency APS quoted the military as saying the 17 freed hostages were "safe and sound."
However, officials refused to comment on the circumstances of their release, citing concerns about the safety of the remaining 15 hostages — 10 Germans, four Swiss and one Dutch.
"We remain highly concerned about those still in the hands of the hostage-takers," German government spokesman Thomas Steg said. "We are concentrating our efforts on them."
German Interior Minister Otto Schily said "there is hope" the remaining hostages "will be free soon."
Austrian President Thomas Klestil sent a telegram of thanks to his Algerian counterpart, Abdelaziz Bouteflika, adding he was impressed by the "prudent way" in which Algerian authorities freed the hostages.
The tourists began disappearing 2½ months ago after setting off in seven separate groups in four-wheel-drive vehicles or on motorcycles, and were last seen near Libya.
In the Algerian capital Wednesday, the Army said the Salafist Group for Call and Combat was responsible for taking the travelers hostage, the official news agency APS reported. The group is on the U.S. State Department's list of terror organizations.
Algerian news reports have said three Saudi envoys of al Qaeda leader Osama bin Laden met with a top leader of the Salafist Group in December.
The Algerian group, known by the French-language acronym GSPC, is one of two main insurgency movements still fighting to topple Algeria's military-backed government and install an Islamic state.
No group ever publicly claimed responsibility for the kidnappings, opening speculation that the seizures could be in retaliation for the conviction in a Frankfurt court of four Algerians for plotting a failed terror attack on a French Christmas market in 2000.
Other theories blamed Islamic rebels battling Algeria's military-backed government for more than a decade, or possibly smugglers active in the area.
German Foreign Minister Joschka Fischer, who met Monday in Algiers with President Bouteflika, publicly acknowledged for the first time Tuesday that the 32 were kidnapped.
The six freed Germans were with German Ambassador Hans Peter Schiff in the Algerian capital of Algiers, the Foreign Ministry in Berlin said. Deputy Foreign Minister Juergen Chrobog was en route to Algeria to escort them back to Germany.
"They are good condition," ministry spokesman Walter Lindner said.
The 10 Austrians spent Tuesday night in an Algiers hospital, exhausted but safe, the Austrian Foreign Ministry said in a statement.
"It's the most beautiful news of the day: The 10 Austrians are alive and safe," Austrian Chancellor Wolfgang Schuessel said Wednesday.
Schuessel said he hoped the relatives of the hostages who remain captive would get similar news soon.
"I wish them courage and confidence in these difficult hours," he said.
The son of 60-year-old Ingo Bleckmann, one of the missing Austrian tourists, told the press agency his father called home during the night.
"He said he was fine, and that he'd tell me everything when he gets home," Nikolaus Bleckmann said.