President Barack Obama on Wednesday proposed background checks on all gun sales and bans on military style assault weapons and high-capacity magazines as part of a package of steps to reduce gun violence in the wake of the Newtown school massacre last month.

With relatives of some of the 20 children killed in the Connecticut rampage looking on, Obama signed 23 executive actions -- which don't require congressional approval -- to strengthen existing gun laws and take related steps on mental health and school safety.

He also called on Congress to reinstate an assault weapons ban that expired in 2004, to restrict ammunition magazines to no more than 10 rounds, and to expand background checks to anyone buying a gun, whether at a store or in a private sale at an auction or convention.

Referring to the young students killed in the Newtown shootings on December 14 and other victims of gun violence, Obama said the nation must do a better job of protecting its children, especially when they are in schools, shopping malls, movie theaters and other public places.

While some of the steps he proposed are given little chance of winning congressional approval in the face of the nation's powerful gun lobby, Obama said all efforts must be made to reduce chronic gun violence in the country.

"This is our first task as a society -- keeping our children safe," the president said, adding that saving even one life would make the changes he seeks worth the effort.

Republicans immediately rejected the Obama proposals as an attack on the constitutional right to bear arms.

"Nothing the president is proposing would have stopped the massacre at Sandy Hook," said a statement by Sen. Marco Rubio, R-Florida, considered an up-and-coming GOP leader. "President Obama is targeting the Second Amendment rights of law-abiding citizens instead of seriously addressing the real underlying causes of such violence."

The powerful National Rifle Association said it would work with Congress to find what it called "real solutions to protecting America's most valuable asset -- our children."

"Attacking firearms and ignoring children is not a solution to the crisis we face as a nation," the NRA said in a statement. "Only honest, law-abiding gun owners will be affected and our children will remain vulnerable to the inevitability of more tragedy."

Gun rights at center of debate

NRA President David Keene said the "Second Amendment is going to survive" Obama's efforts on gun control.

"What we want to see is what they really have in mind. They've got bullet points. There's going to be a lot more to it than that," Keene said on CNN's "The Situation Room with Wolf Blitzer."

Obama called accusations that he seeks to violate gun rights untrue, saying opponents want to wage a campaign of intimidation and fear instead of working with him for needed changes.

"We can respect the Second Amendment while keeping an irresponsible law-breaking few from inflicting harm on a massive scale," he said.

Gun control supporters, including relatives of shooting victims, lauded Obama's proposals as a good first step to reduce gun violence and urged legislators to take on the difficult issue instead of reverting to partisan postures.

"When you are disheartened by the number of steps that have to be taken, by the fears of gun advocates, by the politics, please dig deep and find new heart," urged Emily Nottingham, the mother of Gabe Zimmerman, the legislative staffer killed in the 2010 Tuscon shooting that disabled Democratic Rep. Gabrielle Giffords of Arizona.

"Think for a moment about your young staffers, your children or grandchildren," Nottingham continued. "Now imagine that that cell phone in your pocket is vibrating and the message says they have been murdered by a stranger with an assault weapon. Imagine that, then shore up your resolve and keep working to protect your staffers, our children, our nation. We need you to not give up."

However, Jerry Henry of the Georgiacarry.org website, which opposes tighter gun controls, told CNN that the Obama proposals were misdirected.

"He did absolutely nothing to address the criminal element," said Henry, who argued that studies show criminals get guns on the street instead of buying them from licensed gun shops that conduct background checks.

Fully enforcing existing gun laws and making criminals serve their full prison terms would do more to halt gun violence, according to Henry, who added that government "cannot legislate evil out of the minds of men."

Polls capture public sentiment

Vice President Joe Biden led a panel assembled by Obama to examine gun control steps after the Newtown shootings, which sparked a fierce public debate over how to prevent such mass killings. Biden's recommendations formed the basis of the package of proposals Obama announced Wednesday.

"The world has changed, and it's demanding action," Biden said at the White House event.

Opponents promise a political fight, with an NRA spokesman saying Tuesday that the group has experienced what he called an "unprecedented" spike in membership numbers since new calls for gun control began in the past month.