Algeria has begun a second military operation to rescue some 30 foreign hostages still captive by al-Qaeda-affiliated group at a gas facility in the country's southeast.
The second round of rescue efforts on Friday come as Algerian state media reported that more than 650 hostages had been freed as part of the army operation.
The state-run APS news agency said 573 of those freed were Algerians. Another 100 were among the 132 foreign workers captured at the In Amenas facility.
The Masked Brigade, an armed group who took hundreds hostage at the In Amenas facility, said on Friday that they would trade captives from the United States for the release of two fighters jailed in the United States.
A spokesman for the group named the two fighters as Aafia Siddiqui, from Pakistan, and Omar Abdel-Rahman, an Egyptian referred to as the "blind sheikh".
The Mauritanian ANI news agency reported that sources close to Mokhtar Belmokhtar, believed to be behind Wednesday's raid, had proposed that France and Algeria negotiate "an end to the war being waged by France in Azawad", northern Mali.
The United States has sent a plane to the Algerian desert where it hopes to transport some of those freed to Europe for medical treatment.
Al Jazeera's Rosiland Jordan, reporting from Washington, said the US has been very cautious to avoid any sign of "US involvement in terms of rescue operations".
Our correspondent said both the White House and the department of state have shown "a real concern about the safety and well-being" of all hostages.
Washington has also been careful to not be seen as sending in troops and giving the "impression of invading another Muslim-majority nation", said Al Jazeera's Jordan.
Of the prisoner swap proposed by the gunmen, Victoria Nuland, state department spokeswoman, said "the United States does not negotiate with terrorists."
The developments come a day after at least 30 hostages and 11 members of the al-Qaeda-affiliated group were killed when Algerian forces stormed the desert gas plant to free the captives.
Eight Algerians and seven foreigners, including two British, two Japanese and a French national, were among the dead, an Algerian security source said.
The military says some of the gunmen who took hundreds of hostages, remain holed up inside.
Stephen McFaul from the Republic of Ireland is one of the foreign nationals who have been released
The hostages include Algerians, as well as foreigners from at least nine countries - including the US, Britain and Japan.
Shinzo Abe, Japanese prime minister, cut short a visit to Indonesia on Friday, reports said, to fly home and deal with the hostage crisis in Algeria in which numerous Japanese are caught up.
The Japanese government criticised the Algerian army for the bloody end to the hostage crisis.
Japan's foreign ministry also summoned the Algerian ambassador demanding answers over the rescue operation.
Yoshihide Suga, the Chief Cabinet Secretary, said: "There is still much confusion in the information but we are receiving reports of casualties.
"We deeply regret the actions taken by the Algerian military."
Mohamed Said, Algerian communications minister, said troops had been forced to act after talks with the kidnappers failed.
Algerian officials say those behind the attack were part of an Al-Qaeda linked group and included Egyptian, Algerian and Tunisian nationals.
The government said it was forced to launch the military operation because the fighters had threatened to blow up the gas plant.
The Masked Brigade said its fighters seized the workers on Wednesday in retaliation for Algeria letting France use its airspace to launch operations against rebels in northern Mali , but security experts said the raid appeared to have been planned well in advance.
The fighters came from Libya, according to the Algerian interior minister.
"According to the information we have, the terrorist group which attacked the In Amenas site came from Libya," Dahou Ould Kablia told Algeria's Arab-language daily Echorouk.