The Kentucky Republican has said, however, that he does not intend to put any gun legislation on the Senate floor unless President Donald Trump says he would sign it into law.
Trump said many areas were under discussion, including background checks.
Democratic lawmakers have been urging a vote on a gun control proposal, pointing specifically to the universal background check bill that already passed the House.
Democratic Senators Joe Manchin and Chris Murphy, along with Republican Senator Pat Toomey, told reporters they had a 40-minute telephone conversation with Trump in which the president was engaged on the issue of gun control.
Republican leaders, who like McConnell are reluctant to endorse any measure without the president expressing a willingness to go along, met with Trump on Tuesday afternoon at the White House.
U.S. Senate Majority Leader Sen.
"We're going to take a look at a lot of different things and we'll be reporting back in a fairly short period of time", Trump said, according to a White House pool report.
"What I am not willing to do is support legislation that will do nothing to make us safer and simultaneously infringes on the rights and liberties guaranteed by our Constitution", said the committee's top Republican, Representative Doug Collins.
"I can assure you the bill. has over 85 percent approval and that's with gun owners and everyone else saying if you go to a commercial transaction, gun show, or on the Internet, don't you think you ought to know who wants to buy that gun and for what goal and what their background is?"
The bills considered in the House this week would ban the sale, possession or manufacture of high-capacity magazines; prohibit those convicted of a hate crime from getting a gun; and give states funding to enforce a federal law requiring that police take firearms from individuals deemed a danger to themselves or others. "Shame on him. There are people who died".
The governors of Pennsylvania, New Jersey and DE are urging President Donald Trump to act on gun handle by supporting a common track record check out bill, and to outlaw assault weapons.
Chelsea Parsons, vice president of Gun Violence Prevention Policy at the Center for American Progress, said she believes there has been significant progress since Congress came back to town.
Votes on that bill and other gun control measures failed in April, 2013.
Sen. Toomey, with a frown, said, "We don't know", when referring to a timeline.
"Background checks on all gun sales are a common-sense solution with overwhelming public support and are a critical step toward stemming the gun violence epidemic in this country", the letter continued.