Kerry told them that the U.S. was looking at different options to help the rebels, but made no promises about any specific types of future aid, said the official, who wasn't authorized to speak publicly on the meeting and demanded anonymity.
The secretary also urged the opposition to organize itself better and said he'd attend a meeting April 20 in Istanbul bringing together the Syrian opposition's big donor nations from Europe and the Arab world, the official said.
Among those who attended Kerry's meeting in London Wednesday were the Syrian opposition's interim prime minister, Hassan Hitto; Vice Presidents Suheir Atassi and George Sabra; Secretary-General Najib Ghadbian; and the opposition's envoys to the United States and Britain.
The new nonlethal assistance package being discussed by administration officials would expand on the $60 million in aid the U.S. announced earlier this year.
That aid included meals and medical supplies for the armed opposition. It marked the first direct American assistance to the opposition forces trying to overthrow Assad, but was greeted unenthusiastically by some rebel leaders, who said it did far too little.
European and Arab nations have been more aggressive in their assistance to the rebels. Britain and France have been shipping the opposition armor, night-vision goggles and other military-style equipment, and are also open to the possibility or arming the rebels.
Arms shipments are also flowing into Syria from Qatar, Turkey and Saudi Arabia.
After meeting with the Syrian opposition leaders, Kerry met with Russian Foreign Minister Sergey Lavrov for talks on the conflict. The U.S. and Russia have frequently been at odds over the Syrian civil war, with Moscow opposing action at the U.N. Security Council that would increase pressure on Assad.
The State Department official said Russia offered no indication that it was softening its position on Syria.
Kerry reiterated the U.S. preference for a political solution that includes Assad leaving power, the official said, and agreed to continuing discussing the situation in Syria with Lavrov and other top diplomats during an evening meeting of the Group of Eight industrialized nations.