Seven hostages were killed by their captors during a final raid by Algerian troops - at least 23 hostages and 32 hostage-takers died in the four-day stand-off, Algerian officials say.
Five Britons are feared dead or missing - five Norwegians are unaccounted for.
US President Barack Obama said blame for the violent outcome rested with the "terrorists" behind the attack.
"We will continue to work closely with all of our partners to combat the scourge of terrorism in the region," said Mr Obama.
President Barack Obama offered on Saturday to provide any assistance the Algerian government needs after a deadly hostage siege at a desert gas plant and said the United States was seeking a "fuller understanding" from Algerian authorities of what took place there.
"The thoughts and prayers of the American people are with the families of all those who were killed and injured in the terrorist attack in Algeria," Obama said in his first comments on the hostage crisis.
Obama's written statement was issued by the White House after the Algerian army carried out a dramatic final assault to end a siege by Islamist militants in which 23 hostages were killed, many of them believed to be foreigners.
The statement made no mention of Americans who were caught up in the hostage crisis. One American has been confirmed dead
Apparently the 44th President doesn't understand how to save the innocent and bring them home alive.