In London, British Foreign Secretary William Hague said talks with rebel military leaders would not involve advice on military tactics or support for their operations. Hague also insisted that Britain would not consider offering weapons to Assad's opponents.
Face-to-face meetings with military figures will take place outside Syria, Hague said. Diplomats from the U.S., Britain, France and Turkey are already scheduled to meet with Syrian opposition groups Thursday in Doha, Qatar, though there has been no announcement that those talks will include discussions with rebel fighters.
He said British diplomats will tell rebel commanders to respect the human rights of captured Assad loyalists, amid concern over abuses carried out by both sides.
"In all contacts, my officials will stress the importance of respecting human rights and international human rights norms, rejecting extremism and terrorism, and working towards peaceful political transition," Hague told lawmakers.
At the Zaatari camp, which houses about 40,000 of the estimated 236,000 people who have fled into Jordan from Syria, Cameron said he would press Obama at the first opportunity to drive forward efforts to end the 19-month-old conflict.
Cameron plans to convene a meeting of Britain's National Security Council in London devoted entirely to Syria and discuss how the U.K. can encourage Obama to pursue a more direct strategy.
"Right here in Jordan I am hearing appalling stories about what has happened inside Syria, so one of the first things I want to talk to Barack about is how we must do more to try and solve this crisis," he said.
Talks with those who had fled the violence had redoubled his "determination that now, with a newly elected American president, we have got to do more to help this part of the world, to help Syria achieve transition," Cameron added.
He flew to the camp by helicopter with Jordanian Foreign Minister Nasser Judeh and announced that Britain would offer an extra 14 million pounds ($22 million) in humanitarian aid, bringing its total funding to 53.5 million pounds ($85.5 million) — making it the second largest donor after the United States.
Cameron later held talks with Jordan's King Abdullah II in the capital, Amman.
Stringer reported from London. Associated Press writer Suzan Fraser in Ankara, Turkey, contributed to this report.