By David Ingram WASHINGTON (Reuters) - U.S. President Barack Obama returned to the subject of mass shootings on Tuesday by proposing to spend millions of dollars more on gun safety programs, inspections of retailers and background checks for people buying firearms. If enacted by a U.S. Congress that has been wary of gun control measures, the $182 million package would advance an issue that rose to the top of the national agenda after the December 2012 shooting of 20 children and six adults at a Newtown, Connecticut, elementary school. The White House put forward the package as part of a proposed budget for the government fiscal year that begins on October 1. Included in the package is $13 million to improve the background check system run by the FBI and $22 million more for the Bureau of Alcohol, Tobacco, Firearms and Explosives, which inspects federally licensed firearms dealers. The ATF has for years lacked the money to inspect all gun shops annually. In 2012, when there were 69,000 firearms retailers, the ATF said it conducted 13,100 inspections. Obama proposed $147 million for states and localities to spend to reduce mass shootings. Of that, $55 million would go to help states submit criminal and mental health records to the FBI's background check system and $2 million would be used "to develop better gun safety mechanisms to prevent the use of firearms by unauthorized users," according to an administration document. The administration proposed spending $75 million on research and pilot projects about school safety, and $15 million for training for "active shooter" situations. In a statement accompanying the budget request, the Justice Department said it was examining all ways at the federal level "to keep firearms away from traffickers and others prohibited by law from possessing firearms." Obama rarely mentioned gun control while campaigning for a second, four-year term in 2012, but a month after he won reelection, the Newtown massacre shocked Americans and altered the administration's priorities. The president ordered a review of possible changes to federal gun laws but ran into opposition from supporters of gun rights. In April, the Senate rejected by six votes a plan to extend background checks to online and gun-show sales. (Editing by Howard Goller and Jim Loney)