Democrats tried to expand background checks to those purchasing weapons at gun shows and through intrastate Internet transactions. They also proposed closing a loophole allowing people on "terror watch lists" to buy guns and explosives.
Both efforts failed in the face of heavy Republican opposition.
Republicans said the government could mistakenly place innocent people on watch lists, denying them their constitutional rights to purchase guns. The influential National Rifle Association has also advanced that argument.
Texas Republican Senator John Cornyn failed to win an alternative putting gun sales on hold for 72 hours for people on watch lists. Critics have said such background checks could take longer to complete.
The FBI is trying to determine whether a couple suspected of the shootings at a workplace in Southern California on Wednesday had links to Islamic militant groups.
In a news conference before the votes, Democratic Senator Richard Blumenthal said: "Congress is complicit in these mass murders when it fails to act."
Blumenthal's home state of Connecticut was the scene of a mass shooting three years ago when a 20-year-old gunman entered an elementary school and killed 20 children and six employees.
After that tragedy, gun control legislation appeared to gain traction, only to fail in 2013 following an emotional Senate debate.
With the latest mass shootings in Paris, as well as in Colorado and California fresh in the public's mind, Democrats argued sentiment was again turning in their favor on gun control.
"I think we are ... reaching a tipping point," New York Senator Charles Schumer said, adding that mass shootings "week after week" were "arousing the American conscience."
But given Thursday's Senate votes and recent public opinion polls, it is not apparent the United States has reached a "tipping point" in favor of stricter gun laws.
A Washington Post/ABC News poll last month found 82 percent thought gun violence was a very serious or somewhat serious problem. But opinion split almost evenly over whether enacting new laws to reduce gun violence or protecting the right to own guns was more important.
The poll also found that 63 percent blamed mass shootings on mental health problems, while 23 percent cited inadequate gun control.
Sanders calls for gun study funding after 1996 vote against similar research
Democratic presidential candidate Bernie Sanders on Thursday urged the funding of gun violence studies at the U.S. Centers for Disease Control and Prevention (CDC), two decades after he voted against funding research into firearms injuries.
"We must authorize resources for the Centers for Disease Control and Prevention to study and research the causes and effects of gun violence in the United States of America," a Sanders campaign email said on Thursday.
The email came a day after 14 people were killed in a shooting in San Bernardino, California.
Congress, at the urging of gun rights supporters, put restrictions on CDC funding of gun research into the federal budget in 1996.
United States Senator Bernie Sanders Source: AAP
Sanders, then a Vermont U.S. representative, voted against an amendment, which ultimately failed, that would have authorized funding for such research, according to the website for the Office of the Clerk of the House of Representatives.
Sanders, now a senator, is vying with front-runner Hillary Clinton and former Maryland Governor Martin O'Malley for the Democratic nomination for the November 2016 presidential election. Gun control has emerged as an issue following a recent series of mass shootings.
Sanders has been dogged by criticism from gun-control groups since entering the presidential race.
While in the House of Representatives, he supported a 2005 federal law that shielded gun manufacturers, distributors and dealers from civil liability for mass shootings, and voted against the 1993 Brady Bill that imposed mandatory background checks and waiting periods for gun purchases.
Residents of Vermont are generally protective of gun rights.
The Sanders campaign did not immediately respond to requests for comment on Thursday. But it has said he favors "sensible gun-control legislation" and that he supported Senate efforts to ban assault weapons and high-capacity magazines after the 2012 mass shooting at an elementary school in Connecticut.
Fifty percent of Democrats support Clinton, the former secretary of state, while 36 percent support Sanders, according to a five-day rolling poll from Reuters/Ipsos dated Tuesday.
