One of the main proposals Obama is poised to adopt would require some unlicensed gun dealers to get licenses and conduct background checks on potential buyers. The change is aimed at occasional dealers, including some who sell online frequently or rent tables at gun shows but do not have a storefront.

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Obama began examining how he could tighten the nation’s gun rules after October’s mass shooting at Umpqua Community College in Roseburg, Ore. Administration lawyers have spent months reviewing various proposals to make sure they can withstand legal challenges.

The idea of requiring informal gun dealers to obtain a license from the Bureau of Alcohol, Tobacco, Firearms and Explosives and of conducting background checks came up two years ago when White House officials drafted a proposal for dealers who sell at least 50 guns annually.

The idea was shelved because of legal concerns but gained new momentum after the Roseburg shooting. At that point, Democratic presidential candidate Hillary Clinton said she would pursue such a requirement by executive action if elected. Administration officials gave the proposal another look and determined it could be done in a way that was legally defensible.

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The White House review has been conducted in relative secrecy, soliciting input from gun safety groups without specifying which policies the administration might ultimately adopt. In the past month, Obama has met with former representative Gabrielle Giffords (D-Ariz.), who was gravely injured in a 2011 mass shooting, and her husband, Mark Kelly, and with former New York City mayor Michael R. Bloomberg and the president of Everytown for Gun Safety, which Bloomberg helped start.

In Obama’s weekly radio address, released a day earlier than usual, the president said he was moving unilaterally because Congress had failed to address the growing problem of gun violence.

“A few months ago, I directed my team at the White House to look into any new actions I can take to help reduce gun violence,” he said. “And on Monday, I’ll meet with our attorney general, Loretta Lynch, to discuss our options.

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“Because I get too many letters from parents, and teachers, and kids to sit around and do nothing,” Obama continued. “I get letters from responsible gun owners who grieve with us every time these tragedies happen; who share my belief that the Second Amendment guarantees a right to bear arms; and who share my belief we can protect that right while keeping an irresponsible, dangerous few from inflicting harm on a massive scale.”

In reviewing its options, the administration has shut out congressional Republicans, who joined with some Democrats in helping block legislation to expand background checks after the 2012 mass shooting at Sandy Hook Elementary School in Newtown, Conn.

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“The administration has not communicated with us, and we have not been briefed,” Doug ­Andres, a spokesman for House Speaker Paul D. Ryan (R-Wis.), said in an email. “We will consider options once we have information, but what seems apparent is none of these ideas would have prevented the recent atrocities. Our focus should be on the consistent causes of these acts — mental illnesses and terrorism — rather than infringing on law-abiding Americans’ constitutional rights.”

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While most Republican presidential candidates did not provide immediate reaction to Obama’s announcement, they are expected to talk about it in the coming days. Former Florida governor Jeb Bush is scheduled to attend a gun show in Orlando on Sunday, where he will discuss the high marks he has received from the National Rifle Association.

Catherine Frazier, a spokeswoman for Sen. Ted Cruz (R-Tex.), said that “President Obama is trying to distract Americans from his failure to address the true threat of radical Islamic terrorism, and instead going after the rights of law-abiding American citizens — it is complete lunacy. If Ted Cruz is elected president, the lawlessness will end on Day One, and Americans’ personal liberties will be restored and protected.”

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Obama will make his case for additional gun restrictions in a number of forums in the coming month, according to aides, including during his Jan. 12 State of the Union address.

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While beefing up background checks has strong support — a Quinnipiac University poll in December found that 89 percent of Americans supported checks for purchases at gun shows and for online sales — Obama’s actions also come as Americans have grown more fearful about the prospect of terrorist strikes and are expressing an openness to having ordinary citizens carry guns.

A Washington Post/ABC News poll conducted last month in the wake of the San Bernardino, Calif., terrorist shootings, for example, found that 53 percent of respondents opposed a ban on assault weapons ban, a record high. When asked which is the better reaction to terrorism, 47 percent said encouraging more people to carry guns legally, while 42 percent preferred enacting stricter gun control laws.

Federal law requires that those who are “engaged in the business” of dealing in firearms to have a federal license — and, therefore, to conduct background checks of potential buyers. But it exempts anyone “who makes occasional sales, exchanges, or purchases of firearms for the enhancement of a personal collection or for a hobby, or who sells all or part of his personal collection of firearms.” The administration wants to narrow that exemption so that more gun sellers will have to get licenses.

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It is unclear how many possible deals a change in the rule would affect, since these activities are not formally tracked and the administration has not disclosed what criteria it has selected to judge which gun sellers would have to register for a federal license.

The guns used in several recent mass shootings — including the ones in Roseburg and Lafayette, La. — were purchased legally, and their buyers were subject to background checks.

Everytown spokeswoman Erika Soto Lamb said the current interpretation of what it means to be “engaged in the business” of selling firearms is “a hazy definition that allows high-volume sellers to transfer thousands of guns without background checks, no questions asked.”

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The administration has been weighing other proposals, including requiring federally licensed gun dealers to report any lost and stolen guns to the National Crime Information Center; providing guidance on restricting dangerous individuals from carrying guns within a specified distance of a school; clarifying that convicted abusers are prohibited from having guns regardless of their marital status; and instructing federal law enforcement to identify and arrest criminals who attempt to buy illegal guns.

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The final package will contain at least half a dozen measures, and possibly more, according to those who have been briefed on it.

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Any action by the president is sure to trigger a major backlash from gun-rights activists and Republican officeholders. Jennifer Baker, an NRA spokeswoman, said in an email that the president “is doing what he always does when he doesn’t get his way, which is defy the will of the people and issue an executive order.”

“This is nothing more than a political stunt to appease anti-gun billionaire Michael Bloomberg and will do nothing to increase public safety,” she said, adding that a dozen high-profile mass shooters passed background checks, including Jared Loughner, who shot Giffords and 19 others in Tucson; Dylann Roof in Charleston, S.C.; and James Holmes in Aurora, Colo.

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Even as Obama made his radio pitch, a Texas law letting licensed handgun owners carry their weapons openly in public took effect.

Texas Gov. Greg Abbott (R) mocked the president’s latest push in a tweet, writing, “Obama wants to impose more gun control. My response? COME & TAKE IT.”

But groups such as MoveOn.org have begun to mobilize firearm owners to support expanded background checks and other measures aimed at curbing gun violence.

David Mark Williams, a farmer in Halfway, Ore., described guns as “a tool. If you’re hunting or living a rural lifestyle, you’re going to have a firearm.” But Williams, who came to Washington this fall with MoveOn.org to meet with members of Congress from both parties, said he resigned his NRA membership after the group’s president opposed stricter gun laws in the aftermath of the Sandy Hook killings.

“I’m also a supporter of rational reasonable gun control measures,” Williams said.

Arkadi Gerney, a senior fellow at the Center for American Progress, a liberal think tank, said in an email Friday that “while public opinion on completely banning particular types guns is more mixed,” there’s no question that an overwhelming majority of Americans “favor proposals, like universal background checks, that are aimed at keeping guns out of the wrong hands. And, notably such measures have been the primary focus of the administration’s legislative and executive action efforts.”

Scott Clement, Ed O’Keefe and Katie Zezima contributed to this report.