Barrack Obama said the US, as the world's number two greenhouse gas emitter, "recognises our role in creating this problem" and "we embrace our responsibility to do something about it".
He called on world leaders to show they also share a sense of responsibility.
"2015 is on pace to be the warmest year of all. No nation - large or small, wealthy or poor - is immune to what this means," Mr Obama said.
The "future is one that we have the power to change right here right now, but only if we rise to this moment," he added.
"If we act here, if we act now, if we place our own short-term interests behind the air that our young people will breathe and the food that they will eat and the water they will drink and the hopes and dreams that sustain their lives, then we won't be too late for them," he told the summit.
As the summit opened, leaders held a minute's silence for the 130 people killed at the Paris terror attacks on 13 November.
French President Francois Hollande told the summit that climate change and terrorism were "two major global challenges that we must overcome".
"We must leave our children more than a world free of terror - we owe them a planet protected from disasters," he told the delegates, adding, "we are at breaking point".
"Never have the stakes of an international meeting been so high, because we are talking about the future of the planet, the future of life," he said.
The talks take place amid unprecedented security in the French capital, where protesters clashed with riot police after a climate march was banned following the attacks.
But more than 600,000 people in 175 countries marched at the weekend to demand a strong deal to curb greenhouse gases.
The last major climate conference five years ago in Copenhagen failed to secure sign-up to a universal target for reducing emissions.
In advance of the Paris talks, 183 nations have submitted individual commitments, large or small, to slow global warming.
The EU has pledged to cut greenhouse gases by at least 40% by 2030, while China has vowed that its emissions will peak by 2030.
These "differentiated responsibilities" allow the world to share an overall goal of limiting emissions by 40-70% by 2050 and 100% by 2100, according to the UN.
Lead negotiator for the UN, Christiana Figueres, said the pledges covered 95% of carbon emissions and would limit the rise in global temperature this century.
"We are no longer (heading for) 4,5 or 6C," she said.
"We are now in the bandwidth of 2.7 to 3.5C. Is that enough? No, because we have to stay under 2C."
The 2C threshold is seen as the safe limit for temperature rise, beyond which the climate becomes dangerously unstable.
But there are still major issues that need to be resolved.
The EU wants any deal to be legally enforceable, but that is being resisted by the US.
And poorer countries that are most vulnerable to climate change want richer nations to pay into a fund to help them adapt to a warmer world.
British PM David Cameron will call for "global action to deal with a global problem."
"We must include a five-yearly review mechanism to increase ambition in the future," he said.
"Whilst emissions reductions should always be pledged country by country, we must review our ambition regularly if we are to hit our final two degree goal."
