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He added that destroying the militant group will take time because of the power vacuum in Syria, the abundance of battle-hardened fighters that grew out of al Qaeda during the Iraq war, and the need to build coalitions, including with local Sunni communities.
Islamic State released a video on Tuesday (local time) showing the beheading of the US journalist, the second American hostage to be killed within weeks, in retaliation for US air strikes in Iraq.
"The bottom line is this, our objective is clear and that is to degrade and destroy (Islamic State) so that it's no longer a threat not just to Iraq but also the region and to the United States," Obama told a news conference.
"Whatever these murderers think they will achieve with killing innocent Americans like Steven, they have already failed," Obama said. "They failed because, like people around the world, Americans are repulsed by their barbarism. We will not be intimidated."
US and British officials both examined the video, showing the same British-accented executioner who appeared in an August 19 video of the killing of US journalist James Foley, concluding it was authentic.
The United States resumed air strikes in Iraq in August for the first time since the pullout of US troops in 2011, and Obama said the strikes are already proving effective.
"Those that make the mistake of harming Americans will learn that we will not forget and that our reach is long and that justice will be served," said Obama, who authorised the strike in Pakistan that killed al Qaeda leader Osama bin Laden 10 years after the September 11, 2001, attacks on the United States.
At home, top Obama administration officials punctuated Obama's warnings to the Islamic State.
"They should know we will follow them to the gates of hell until they are brought to justice. Because hell is where they will reside, hell is where they will reside," Vice President Joe Biden said during an appearance in New Hampshire.
In Washington, Secretary of State John Kerry called Sotloff's execution a "punch to the gut" and said the United States has used every military, diplomatic and intelligence tool it has to free hostages in Syria.
Kerry said Sotloff was "brutally taken from us in an act of medieval savagery by a coward hiding behind a mask."
"We have taken the fight to this kind of savagery and evil before and, believe me, we will take it again," he said. "When terrorists anywhere around the world have murdered our citizens, the United States held them accountable no matter how long it took."
Obama is sending Kerry, Defense Secretary Chuck Hagel and counterterrorism adviser Lisa Monaco to the Middle East to work with regional partners on ways to battle Islamic State.
"This is not going to be a one-week or one-month or six-month proposition because of what's happened in the vacuum of Syria," Obama said. "It's going to take time for us to be able to roll them back."