A senior administration official told reporters the price tag for the entire package was $500 million.
Obama also said he would nominate B. Todd Jones, the acting director of the Bureau of Alcohol, Tobacco, Firearms and Explosives, to become its permanent chief. The agency has been without a full-time director for six years.
A main focus of Obama's steps was closing loopholes in background checks. While requiring universal background checks would require congressional approval, some of the executive actions signed by Obama were intended to bolster the existing system.
Across the country, more than a million people failed background checks to buy guns during the past 14 years because of criminal records, drug use or mental health issues, according to FBI figures.
That figure, however, is a small fraction of overall gun sales.
Obama also called for more money to strengthen gun safety at schools, including hiring more counselors such as retired law enforcement officers to help educate students on gun issues. He also called for more funding for communities to hire more police officers, but stopped short of seeking the NRA's proposal for armed guards at every school.
Legislators said working with Congress will be paramount in curbing gun violence. California Rep. Mike Thompson told CNN on Tuesday that a ban on high-capacity magazines could garner Republican support, but a full-scale assault weapon ban would be hard to get passed in the GOP-controlled House.
House and Senate committees said they would start holding hearings on gun control measures in coming weeks.
In New York, Democratic Gov. Andrew Cuomo on Tuesday signed into law a series of new gun regulations -- the nation's first since the Newtown shootings.
Both New York's GOP-controlled Senate and Democrat-controlled Assembly approved the measure by overwhelming margins.
It includes a statewide gun registry and adds a uniform licensing standard across the state, altering the current system, in which each county or municipality sets a standard.
Residents are also restricted to purchasing ammunition magazines that carry seven bullets, rather than 10.
"The changes in New York are largely cosmetic," said CNN legal analyst Paul Callan, who described state's existing regulations as "the toughest gun laws in the United States."
Lawmakers in at least 10 other states are reviewing some form of new gun regulations in the new year.