However, the president said US troops would be not be sent back to Iraq.
The US has already made humanitarian air drops to Iraqis under threat from Islamic State (IS) militants.
IS has seized Qaraqosh, Iraq’s biggest Christian town, prompting residents to flee.
‘Coming to help’
Speaking at the White House on Thursday evening after meetings with his national security advisers, Mr Obama said US military aircraft had dropped food and water to members of the Yazidi religious minority community who were trapped on Mount Sinjar by the IS fighters.
Officials had warned that the Yazidis faced starvation and dehydration if they remained on the mountain, and slaughter at the hands of the IS if they fled.
“The US cannot and should not intervene every time there is a crisis in the world,” Mr Obama said.
But he said the US could not turn a “blind eye” to the prospect of violence “on a horrific scale”, especially when the Iraqi government had requested assistance.
“We can act, carefully and responsibly, to prevent a potential act of genocide,” he went on. “Today America is coming to help.”
He said that US air strikes would target IS fighters, should the militants’ convoys move toward Irbil, where there is a significant presence of US diplomats and military advisers, or threaten Baghdad.
In addition, he authorised strikes “if necessary” to help Iraqi government forces break the siege at Mount Sinjar and rescue the trapped civilians.
He added that the US could and should support moderate forces that could bring stability to Iraq, and he said there was no “American solution” to the turmoil plaguing Iraq.
“The only lasting solution is reconciliation among Iraqi communities and stronger Iraqi security forces,” he said.
Analysis: Tom Esslemont, BBC News, Washington
For a president still busy withdrawing his troops from Afghanistan, the situation in northern Iraq has proved decisive.
Doing nothing here was not an option and the US could not turn a blind eye to what Mr Obama called the systematic destruction of Christians and Yazidis.
He employed strong language to seek justification. It was, he said, to prevent acts of genocide.
It is a hugely symbolic and potent term for a president who a year ago decided against military intervention in Syria.
And that was after a red line had been crossed and chemical weapons had been used.
This time, just across the border, the White House has a specific goal – the protection of US assets and embassy personnel in Iraq and to bring urgent relief to the civilians affected.
But to critics it is too limited an operation that will do little to diminish the power of the Islamic State jihadists.
UN: ‘Deeply appalled’
The president spoke hours after the UN Security Council met to discuss the situation.
“The members of the Security Council call on the international community to support the government and people of Iraq and to do all it can to help alleviate the suffering of the population affected by the current conflict in Iraq,” said UK Ambassador to the UN Mark Lyall Grant.
UN Secretary-General Ban Ki-moon said he was “deeply appalled”.
Meanwhile, the US has warned that the situation for Iraq’s minority groups is threatening to become a “humanitarian catastrophe”.
IS, a Sunni Muslim group formerly known as Isis, has been gaining ground in northern Iraq since it launched its onslaught in June. It also controls parts of Syria.
IS says it has created an Islamic state in the territory it controls.
In other developments:
As many as 100,000 Christians are believed to have fled their homes ahead of the IS advance, and most of them are thought to have gone toward the autonomous Kurdistan Region.
Kurdish forces, known as the Peshmerga, have been fighting the IS militants’ advance in the area around Qaraqosh for weeks, but on Wednesday night it appeared they had abandoned their posts.
“It’s a catastrophe, a tragic situation: tens of thousands of terrified people are being displaced as we speak,” said Joseph Thomas, the Chaldean archbishop of the northern city of Kirkuk.
Eyewitnesses in Qaraqosh said IS militants were taking down crosses in churches and burning religious manuscripts.
Pope Francis has made an impassioned appeal to the international community to do much more to address the crisis.
Canon Andrew White: “The international community has got to wake up to the needs of the people”
Last month, hundreds of Christian families fled nearby Mosul after the Islamist rebels gave them an ultimatum to convert to Islam, pay a special tax, or be executed.
Iraq is home to one of the world’s most ancient Christian communities, but numbers have dwindled amid growing sectarian violence since the US-led invasion in 2003.
About 50,000 Yazidis, meanwhile, are thought to have been trapped in the mountains after fleeing the town of Sinjar over the weekend – although the UN says some of them have now been rescued.
Almost 200,000 civilians have been displaced from Sinjar town, the UN Office for the Coordination of Humanitarian Affairs has warned.
Those trapped on the mountain are facing dehydration, and 40 children are reported to have died already.