He has tasked Vice President Joe Biden with co-ordinating the campaign and said he will push through legislation without delay. The President urged Congress to hold votes on the bill.
Mr Obama said the issue was complex but added: "We have a deep obligation, all of us, to try."
Mr Biden, a long-time gun control advocate, will lead a team that will include members of Mr Obama's administration and outside groups.
The move comes after Friday's shooting at Sandy Hook Elementary School in Connecticut, when 20 children and six adults were killed by a gunman with a semi-automatic rifle.
Mr Obama said: "The fact this problem is complex can no longer be an excuse for doing nothing. The fact we can't prevent every act of violence doesn't mean we can't steadily reduce the violence."
His call at a White House briefing came as more funerals were held for the victims, including the first service for a teacher.
In Stratford, Connecticut, hundreds of mourners stood in line more than an hour before the funeral service of hero teacher Victoria Soto, 27, who died after saving her pupils by herding them into a bathroom.
In front of the Lordship Community Church, three men played the bagpipes, wearing red and green kilts. More than 20 police officers lined up outside of the church wearing yellow shoulder sashes.
Police chief Gary McNamara said one of his department's officers was Ms Soto's cousin and added officers dealt with personal tragedy by "leaving their hearts at home or in their police cars" before resuming their jobs.
Funerals were also held for pupils Daniel Barden, seven, Caroline Previdi, six, and Charlotte Bacon, six.
Mr Obama, who pushed little on gun control during his first term, pressed Congress to reinstate a ban on assault weapons and high-capacity magazines, which expired in 2004.
He also called for stricter background checks for people who seek to purchase weapons.
The administration will have to make its gun control push in the middle of tense negotiations with Congress to avoid the "fiscal cliff" of billions of dollars in tax increases and deep spending cuts that will kick in at the end of the year without a deal.
The shooting has prompted several Congressional gun-rights supporters to consider new legislation to control firearms, and there are concerns in the administration and elsewhere that their willingness to engage could fade as the shock and sorrow over the shooting eases.
The most powerful backer of gun owners and the gun industry, the National Rifle Association, broke its silence four days after the shooting. In a statement, it pledged to "help to make sure this never happens again".
With the NRA promising "meaningful contributions" and Mr Obama vowing "meaningful action", the challenge in Washington is to turn words into deeds. Ideas so far have ranged from banning people from buying more than one gun a month to arming teachers.
The challenge will be striking the right balance with protecting the Second Amendment right to bear arms. Firearms are in one-third or more of US households and suspicion runs deep of an overbearing government whenever it proposes expanding federal authority.
Many pro-gun politicians have also called for a greater focus on mental health issues and the impact of violent entertainment such as video games. Mr Obama prefers a wider approach, with aides saying stricter gun laws alone are not the answer.
Mr Obama said the US needs to make access to mental health-care as easy as access to a gun.
However, much of the immediate focus is on gun control, an issue that has been dormant in Washington for years despite several mass shootings.
The policy process Mr Obama announced was expected to include input from the departments of Justice, Education, and Health and Human Services.
The Department of Homeland Security is also expected to play a key role.