The package proposed Wednesday is the most comprehensive in decades. The president called for a new, tougher assault weapons ban and a 10-round limit on magazines, as well as legislation to bar the possession of armor-piercing bullets and require criminal background checks for nearly all gun sales.
Separately, he approved 23 executive actions while calling for additional funding to address mental health and school security.
The movement comes in the wake of last month's school massacre in Connecticut, where 20 children and six adults were killed.
"If there's even one life that can be saved, then we've got an obligation to try," said Obama, joined at the White House by four children who wrote to the president following the Newtown, Conn., tragedy.
But several lawmakers said the president's proposals in large part would not have prevented a shooting like the one at Sandy Hook Elementary School. They accused the president of glossing over potential factors like the entertainment industry and the country's mental health system, making clear that the legislative proposals could face an uphill climb.
"Nothing the president is proposing would have stopped the massacre at Sandy Hook. President Obama is targeting the 2nd Amendment rights of law-abiding citizens instead of seriously addressing the real underlying causes of such violence," Sen. Marco Rubio, R-Fla., said. "Rolling back responsible citizens' rights is not the proper response to tragedies committed by criminals and the mentally ill."
Sen. Charles Grassley, R-Iowa, said the proposals would merely invite "drawn-out court battles."
"Instead of a thoughtful, open and deliberate conversation, President Obama is attempting to institute new restrictions on a fundamental constitutional right," he said.
Texas Gov. Rick Perry, in a written statement, said: "Guns require a finger to pull the trigger. The sad young man who did that in Newtown was clearly haunted by demons, and no gun law could have saved the children in Sandy Hook Elementary from his terror."
But both sides of the debate were preparing Wednesday for a drawn-out national debate. The National Rifle Association is preparing to launch a major ad campaign and has already started running one ad. The group said Wednesday it would work with Congress on a "bipartisan basis" but that "attacking firearms and ignoring children is not a solution to the crisis we face as a nation."
The NRA said: "Only honest, law-abiding gun owners will be affected, and our children will remain vulnerable to the inevitability of more tragedy" as a result of the administration's plan.
On the other side, a group founded by former Rep. Gabrielle Giffords, who was wounded in a 2011 mass shooting, and her husband, Mark Kelly, has gotten involved in making the public case for gun control. Kelly and Vice President Biden, who led the president's anti-gun violence task force, met Wednesday in Washington.
A handful of Democratic lawmakers have already proposed gun-control bills, though Obama on Wednesday did not endorse any specific piece of legislation. Senate Judiciary Committee Chairman Patrick Leahy said he plans to start holding hearings in two weeks on the issue.
Sen. Dianne Feinstein, D-Calif., who intends to introduce a gun-control package next week including an assault-weapons ban, on Wednesday praised the president's announcement.
"He was exactly right when he said 'weapons designed for the theater of war have no place' in our society. I couldn't agree more. These weapons have one purpose: to kill the most people in the shortest amount of time possible," Feinstein said.
The leaders of the House and Senate declined to issue any definitive statements on Wednesday. "House committees of jurisdiction will review these recommendations. And if the Senate passes a bill, we will also take a look at that," said Michael Steel, spokesman for House Speaker John Boehner.
In the Senate, Democratic Leader Harry Reid said: "I am committed to ensuring that the Senate will consider legislation that addresses gun violence and other aspects of violence in our society early this year." He thanked the task force for the "thoughtful" ideas and said "all options should be on the table moving forward."
The president, immediately after making his remarks, signed nearly two-dozen executive actions -- a step that has stirred objections from lawmakers who have warned Obama not to overstep his bounds.
Unilaterally, Obama on Wednesday directed federal agencies to share information with the federal background check system; proposed new rules to let law enforcement run full background checks before returning a seized gun; ordered the Centers for Disease Control to research causes of gun violence; required law enforcement to trace guns from criminal investigations; and took other steps. Obama also is nominating the ATF's acting director, Todd Jones, to lead the agency permanently.
The most controversial elements of the president's plan, though, continue to be the proposals he wants Congress to pass.
The call for universal background checks would extend to gun shows and private sales, with "limited" exemptions for "certain transfers" among family members and other situations. The administration plans to give private sellers guidance on how to run background checks as soon as possible.
The president also wants to commit $4 billion to hiring more police officers and to pass new gun trafficking laws to explicitly prohibit straw purchasing.
The White House plan addresses school security, as well, urging Congress to help schools complete emergency plans; proposing an initiative to help schools hire up to 1,000 resource officers and mental health professionals. and proposing new training for teachers to recognize mental health issues among young people. Obama also plans to beef up mental health insurance coverage by executive action.