The US Senate's strongest push in years to tighten gun controls is likely to fall short.
US lawmakers are trying to forge a compromise later this week that might keep firearms away from people on terrorism watch lists.
The deadliest mass shooting in modern US history spurred quick action in Congress, but none of Monday's bills are expected to achieve the 60 votes needed for passage in the 100-seat chamber, as Republicans and Democrats have not been able to reach consensus.
Republicans and Democrats have offered four separate proposals to expand background checks on gun buyers and curb gun sales for individuals on terrorism watch lists after last week's massacre in an Orlando nightclub.
Senator Chris Murphy, who led fellow Democrats in 15 straight hours of floor debate last week to demand action on gun control, acknowledged that an amendment of his to require background checks for gun sales may not win approval in the Republican-controlled Senate.
"I admit that the background checks bill is going to be tough to get 60 votes on, but we still have hope that we can get Republicans to support the bill stopping terrorists from getting weapons," Murphy, from Connecticut, told ABC's This Week on Sunday.
While gun control efforts failed after mass shootings at an elementary school in Newtown, Connecticut in 2012 and a conference centre in San Bernardino, California in 2015, some senators see resistance to gun restrictions softening as national security looms larger in the debate.
The Orlando gunman, Omar Mateen, pledged allegiance to the militant group Islamic State as he killed 49 people in a gay nightclub.
A Reuters/Ipsos poll conducted last week found that 71 percent of Americans favour at least moderate regulations and restrictions on gun sales. That compared with 60 percent in late 2013 and late 2014.
The United States has more than 310 million weapons, about one for every citizen.
Separately, the Supreme Court on Monday rejected a challenge by gun rights advocates, leaving in place gun control laws in New York and Connecticut that ban assault weapons like the one used in last week's massacre in Florida.
The issue has also moved to the forefront of the debate ahead of the November 8 US election.
Republican presidential candidate Donald Trump on Monday sought to clarify comments he made about guns following the Orlando shooting, saying in a tweet that he meant security staff -- not patrons -- at the gay nightclub should have been better armed.