But in a change of emphasis, the mainly Western and Arab "Friends of Syria" group meeting in Rome "underlined the need to change the balance of power on the ground".
A final communique said participants would "coordinate their efforts closely so as to best empower the Syrian people and support the Supreme Military Command of the (rebel) Free Syrian Army in its efforts to help them exercise self-defense".
More than 70,000 Syrians have been killed in a fierce conflict that began with peaceful anti-Assad protests nearly two years ago. Some 860,000 have fled abroad and several million are displaced within the country or need humanitarian assistance.
Kerry, after the talks in Rome, said Washington would more than double its aid to the Syrian civilian opposition, giving it an extra $60 million to help provide food, sanitation and medical care to devastated communities.
The United States would now "extend food and medical supplies to the opposition, including to the Syrian opposition's Supreme Military (Council)", Kerry said.
In their communique, the "Friends of Syria" pledged more political and material support to the Syrian National Coalition, a fractious Cairo-based group that has struggled to gain traction inside Syria, especially among disparate rebel forces.
Riad Seif, a coalition leader, said before the Rome meeting that the opposition would demand "qualitative military support".
Another coalition official welcomed the result of the talks. "We move forward with a great deal of cautious optimism. We heard today a different kind of discourse," Yasser Tabbara said.
But the continued U.S. refusal to send weapons may compound the frustration that prompted the coalition to say last week it would shun the Rome talks. It attended only under U.S. pressure.
Many in the coalition say Western reluctance to arm rebels only plays into the hands of Islamist militants now widely seen as the most effective forces in the struggle to topple Assad.
However, a European diplomat held out the possibility of Western military support, saying the coalition and its Western and Arab backers would meet in Istanbul next week to discuss military and humanitarian support to the insurgents.
MEALS READY TO EAT
Kerry's offer of medical aid and Meals Ready to Eat (MREs), the U.S. army's basic ration, fell far short of rebel demands for sophisticated anti-tank and anti-aircraft weapons to help turn the tables against Assad's mostly Russian-supplied forces.
It also stopped short of providing other forms of non-lethal assistance such as bullet-proof vests, armored personnel vehicles and military training to the insurgents.
Last week the European Union opened the way for direct aid to Syrian rebels, but did not lift an arms embargo on Syria.
The Rome talks again signaled the lack of appetite among the United States and its allies for direct military intervention in Syria, after the withdrawal of U.S.-led troops from Iraq and the drawdown under way in Afghanistan.
The communique called for an immediate halt to "unabated" arms supplies to Damascus by third countries, referring mostly to Assad's allies Russia and Iran.
It also said Syria must immediately stop indiscriminate bombardment of populated areas, which it described as crimes against humanity. NATO officials say Assad's military has fired ballistic missiles within Syria, which the government denies.
Human Rights Watch has reported that at least 171 civilians were killed in four Scud missile strikes last week.
The "Friends of Syria" pledged "more political and material support to the coalition as the sole legitimate representative of the Syrian people and to get more concrete assistance inside Syria", but gave no details on exactly what would be provided.
Kerry said earlier this week he would not leave the Syrian opposition "dangling in the wind", unsure of getting support.
But the White House continues to resist providing weaponry to the rebel forces, arguing there is no way to guarantee the arms might not fall into the hands of Islamist militants who might eventually use them against Western or Israeli targets.
U.S. officials have said that the U.S. Defense and State departments, under former Secretary of Defense Leon Panetta and former Secretary of State Hillary Clinton, privately recommended that the White House arm the rebels, but were overruled.
"It's a huge debate inside the administration between those that have to deal with Syria on an everyday basis, the State Department and DoD (Defense) particularly, and the White House, which ... until now has vetoed any kind of outreach to the armed groups," said Andrew Tabler, senior fellow at the Washington Institute for Near East Policy, a think-tank.
The United States says it has already provided more than $50 million in non-lethal assistance such as communications gear and governance training to Syria's civilian opposition.
A source in the Syrian coalition, however, said even the extra $60 million promised by Washington was a pittance compared to what he said was the $40 million a day in humanitarian aid needed for Syrian refugees and internally displaced persons.
The United States has provided some $365 million in humanitarian aid for Syrian refugees in countries such as Turkey, Jordan and Lebanon and for internally displaced people, channeling this money through non-governmental organizations.
More than 40,000 people a week are fleeing Syria and the total number of refugees will likely pass 1 million in less than a month, far sooner than the United Nations had forecast, a senior U.N. official told the Security Council on Wednesday.
U.N. High Commissioner for Refugees Antnio Guterres said his agency had registered 936,000 Syrians across the Middle East and North Africa, nearly 30 times as many as in April last year.
"We expected to have 1.1 million Syrian refugees by June. If things continue to accelerate like this, it will take less than a month to reach that number," he told the 15-member council.
(Writing by Alistair Lyon; Editing by Mark Heinrich)