The U.S. Senate on Thursday voted to open debate on gun control measures advocated by President Barack Obama and mostly Democratic lawmakers, clearing the first hurdle for relevant legislation.

In a 68-31 vote, the upper chamber of the U.S. Congress approved a procedural motion that will allow debate on the floor over the most ambitious gun control legislation in more than a decade. The move will set off weeks of debate in the Senate.

The Obama administration "strongly supports" the Senate package of gun control measures," which takes critical steps to reduce the epidemic of gun violence in the nation," according to a statement released by the White House on Thursday.

The White House welcomed the development, said White House spokesman Jay Carney at the daily briefing. Yet he stressed that this "very important" move remains to be "a first stage" in efforts to get "sensible, common-sense" gun control legislation passed on the Capitol Hill.

The Senate vote came nearly four months after 20 schoolchildren and six educators were killed in the Sandy Hook Elementary School mass shooting, which occurred in Newtown, Connecticut. The massacre has shocked the nation and renewed the gun control debate.

Connecticut Governor Dannel Malloy signed a strict and sweeping gun control legislation of the state last week. But legislation at federal level has met much more resistance.

The Senate package of measures include providing more school safety aid, expanding federal background checks on gun sales and strengthening prosecution of illegal gun traffickers.

"The measures in this bill are common-sense solutions that in no way infringe on the Second Amendment rights of law-abiding gun owners and that have the strong support of the American people," said the White House statement.

However, Obama and the Democratic lawmakers who lead the issue have yet failed to translate public support for some key parts of the 'common-sense solutions' into momentum for gun control legislation.

The universal background checks for all gun sales, a measure that over 90 percent of Americans now support according to the Quinnipiac University poll, had seemed to be in trouble during Senators' gun-control negotiation. Republican Senator Pat Toomey and Democrat Senator Joe Manchin announced on Wednesday an agreement on background checks for gun purchases, serving as a last-minute boost to the gun control legislation.

"Over the past 14 years, the existing system has been effective at keeping more than two million guns out of the wrong hands, but this expansion is necessary to close loopholes that allow criminals and other dangerous individuals to avoid background checks entirely," said the White House in the statement.

Senate Majority Leader Harry Reid also dropped the renewal of the federal assault weapons ban in the whole package, which signaled the measure and even the overall gun control package still lacked enough support in Congress.

Obama is currently trying to build momentum for gun control legislation at the national level through a series of public events. He has launched a new round of all-out gun control campaign this week, starting from a high-profile speech in Connecticut where is still feeling the pain of the December shooting massacre. He also brought back families of the victims to the capital on Air Force One, the presidential plane to join the gun control lobby on Capitol Hill over the past two days.

"Imagine what they would say to the families of victims in Newtown about why a certain measure never came to a vote because they filibustered it," said Carney earlier this week.

However, the gun control legislation still face an uncertain path in both chambers of Congress and lawmakers still face sustained pressure from gun rights groups.

The National Rifle Association, the nation's largest gun rights organization and lobby group, "unequivocally opposed" to the Senate bill, said its chief lobbyist Chris Cox in a letter to senators on Wednesday.

The group was one of the main forces to successfully block the efforts to extend the 10-year federal assault weapon ban which expired in 2004.