Senate Majority Leader Harry Reid, D-Nev., speaks with reporters after a weekly Democratic strategy session, at the Capitol in Washington, Tuesday, Jan. 29, 2013. (J. Scott Applewhite/AP)

The Senate’s top Democrat offered fresh details Sunday about his position in the renewed debate over guns, as he endorsed expanding background checks on gun sales and promised to consider bans on assault-style weapons and high-capacity ammunition magazines.

“Everyone acknowledges we should do something with background checks,” Majority Leader Harry M. Reid (D-Nev.) said in an interview on ABC News’s “This Week With George Stephanopoulos.”

While Reid pronounced his support for expanding background checks on gun purchases, he said he was undecided about proposed bans on assault-style weapons and high-capacity ammunition magazines.

“I didn’t vote for the assault weapons last time because it . . . didn’t make sense,” Reid said. Nonetheless, Reid said he plans to “take a look” at the latest proposal. And imposing new restrictions on high-capacity magazines is “something we definitely have to take a look at,” he said.

Reid’s support for expanding background checks is a boost to the gun-control measure that appears to stand the best chance of garnering broad support on Capitol Hill. A bipartisan group of senators has been working on a proposal to expand background checks, and polls show that most Americans support mandating background checks for all gun sales. Under current law, sales involving licensed gun dealers require background checks, but those between private citizens do not.

By comparison, it’s been much more difficult for gun-control advocates to build consensus around a proposed assault weapons ban, which a group of Democratic lawmakers introduced last month. It’s not just Republicans who are likely to oppose the ban; Democrats facing reelection in conservative states next year could face intense criticism from gun rights groups over a vote in favor of the measure, which might prompt some of them to oppose it.

The nation’s largest gun rights group, the National Rifle Association, staunchly opposes universal background checks. NRA Executive Vice President Wayne LaPierre warned on “Fox News Sunday” that requiring universal checks would lead to “a “universal registry of law-abiding people.”

Reid is the recipient of a “B” rating from the NRA, a better mark than most Senate Democrats. “I know Wayne LaPierre; he’s always been extremely pleasant to me,” Reid said, but “just because they resist it doesn’t mean we can’t do things.”

As the gears turn in Congress, President Obama will make his latest push for stricter gun-control laws in a Monday appearance in Minneapolis, where he will meet with local leaders and law enforcement officials and deliver remarks. The president last month unveiled a sweeping slate of new gun-control proposals including a call for Congress to pass laws requiring background checks and banning assault-style weapons and high-capacity magazines.

The White House released a photo Saturday of Obama skeet shooting at Camp David last summer. The president was recently asked by the New Republic magazine whether he had ever fired a gun. “Yes, in fact, up at Camp David, we do skeet shooting all the time,” the president responded, prompting an outpouring of questions about whether the White House could validate the claim.

The Senate Judiciary Committee last week called witnesses to testify at a hearing. LaPierre appeared before the committee, as did Gabrielle Giffords, who survived an assassination attempt as a congresswoman in 2011.

Giffords and her husband, former astronaut Mark Kelly, recently announced the formation of a group designed to counteract the influence of the NRA. On Sunday, Kelly kept up his push for new gun-control measures, citing the mass shooting at a Newtown, Conn., elementary school as a reason to take urgent action.