British Prime Minister David Cameron on Monday called for greater efforts to end the protracted conflict in Syria, stressing that "there is no more urgent international task than this."

At a joint press conference with U.S. President Barack Obama following their talks at the White House, Cameron said that they both welcomed Russian President Vladimir Putin's commitment to push jointly for a political solution to the 27-month conflict in the Middle East country.

"We need to get Syrians to the table to agree a transitional government that can win the consent of all of the Syrian people," he added.

The United States and Russia have agreed to sponsor another conference in Geneva by the end of May -- bringing to the table representatives of the Syrian government and the opposition -- to make a fresh bid for peace. Cameron has described his meeting with Putin last week as "extremely positive."

"There is now, I believe, common ground between the U.S., UK, Russia and many others that whatever our differences, we have the same aim -- a stable, inclusive and peaceful Syria, free from the scourge of extremism," said the British leader. "There is real political will behind this. We now need to get on and do everything we can to make it happen."

Citing the rising death toll in the Syrian crisis, Cameron said: "The world urgently needs to come together to bring the killing to an end."

"None of us have any interest in seeing more lives lost, in seeing chemical weapons used, or extremist violence spreading even further," he noted. "The challenges remain formidable, but we have an urgent window of opportunity before the worst fears are realized."

For his part, Obama vowed to continue to press Syrian President Bashar al-Assad to step down to usher in a political transition in the country. He also said that Washington and London will continue to try to establish the facts about the alleged use of chemical weapons in Syria before taking next steps.

On Russia's role, Obama said: "As a leader on the world stage, Russia has an interest as well as an obligation to try to resolve this issue in a way that can lead to the kind of outcome that we'd all like to see over the long term."

Both Obama and Cameron pledged to continue with the efforts to strengthen what they called "the moderate opposition" in Syria. Cameron said that his country was pushing for a relaxation of the EU arms embargo on Syria to make way for arming the opposition forces.

However, the two leaders said that so far no decision has been made regarding arming the Syrian rebels.

The Obama administration has limited its aid to the Syrian opposition to humanitarian and non-lethal supplies, fearful of any weapons falling into the hands of Islamist militants in the country.

Cameron said that Britain would double its "non-lethal" support to the Syrian opposition in the coming year, including armored vehicles, body armor and power generators.

The sense of urgency over the Syrian conflict has heightened following the recent allegations of chemical weapons use in the country and reported Israeli air raids on targets inside of Syria.

The fresh U.S.-Russia proposal for another conference in Geneva is seen as an attempt to build on the Geneva Communique adopted late last June by the five permanent members of the UN Security Council and four Middle East countries, which envisaged the establishment of a transitional governing body in Syria to lead a political transition there.

In his visit to Russia last week, U.S. Secretary of State John Kerry said that the communique should be treated not simply as a piece of paper, but "as a road map to a new Syria without violence. "