Story highlights French President Francois Hollande says he has assurances Algeria will seek justice

Herve Gourdel, in his late 50s, was a mountaineer

France won't back down against terrorism, Hollande says

President Obama issues condolences for beheaded French hostage

French hostage Herve Gourdel was abducted and beheaded, a killing shown on video, French President Francois Hollande told the United Nations General Assembly on Wednesday.

"You will understand that today I am speaking before you with a particularly high level of emotion because one of my compatriots has just been subject of a cowardly assassination," Hollande said. "He was a man who was full enthusiasm. He loved the mountains. He thought he would be able to pursue his passion moving into the Ouzou area in Algeria."

Hollande said the attack won't affect France's role in the battle against terrorism.

"France will never give in to blackmail, to pressure, to barbaric acts. Quite to the contrary, France knows what is expected," Hollande said.

Earlier, Hollande expressed his condolences to Gourdel's family in a news conference at the French mission.

Gourdel was kidnapped over the weekend in Algeria's Tizi Ouzou region east of Algiers, the French Foreign Ministry said. The video was posted online Wednesday. It shows armed men who claim to belong to Islamist militant group Jund al-Khilafa -- or Soldiers of the Caliphate -- in Algeria. They pledge allegiance to Abu Bakr al-Baghdadi , the leader of the Islamic State in Iraq and Syria.

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Titled "A message of blood for the French government," the video surfaced as French Prime Minister Manuel Valls addressed the French National Assembly, the country's lower house of parliament, about the fight against ISIS.

France is part of a broad coalition that is working with the United States to combat the brutal extremist group.

According to his website, Gourdel was born in 1959 and when he was a teenager decided he wanted to become a mountain guide. He opened a guide office in Saint Martin-Vésubie in 1987 where he spent more than 20 years, the website says. He was also an active member of a mountaineering club that spent time in France's Mercantour National Park.

The Algerian government called the beheading an act of "criminals."

"It is with a lot of sorrow and sadness that the Algerian government has learned about the horrible assassination of French national Pierre Hervé Gourdel, an odious and despicable act committed by a group of criminals," officials said, according to the state-run Algerie Presse Service news agency.

Hollande said he spoke with Algerian Prime Minister Abdelmalek Sellal, who assured Hollande he would commit a maximum effort to find the killers and Gourdel's body.

"We owe it to his family," Hollande said.

The video appears to show the latest beheading of a Westerner by an Islamist extremist group. Since mid-August, ISIS has beheaded American journalists Steven Sotloff and James Foley and British aid worker David Haines.

The new video came on the same day U.S. President Barack Obama addressed the United Nations, calling for all countries to unite against terrorism and brutality wrought by ISIS. The Islamic State in Iraq and Syria goes against everything Islam stands for, he said. Islam, Obama said, is about peace.

Obama publicly extended the condolences of the United States to the people of France for the death of Gourdel.

The U.N. Security Council issued a statement condemning the "heinous and cowardly murder."