Kerry also spoke of "mutual" agreement among Syrians, but one that excluded Assad. "We see only one option - negotiating a transition government born by mutual consent," he said. "That means that Bashar al-Assad will not be part of that transition government."
Despite the differences, however, some participants believe common interests in reining in violence could rally the West, Russia and possibly even Iran behind some form of compromise.
A last-minute invitation from Ban to Iran was revoked after the Syrian opposition threatened to boycott the talks - a move that threatened to undermine months of US and Western efforts to cajole Jarba's National Coalition into taking part.
President Hassan Rouhani said from Tehran that Iran's exclusion made it unlikely the conference could succeed.
WAR RAGES IN SYRIA
During the speeches in Montreux, the war went on in Syria.
The Syrian Observatory for Human Rights monitoring group reported clashes and air strikes around the country. Around Damascus, government artillery hit villages and rebels clashed with the army in the neighbourhood of Jobar on the northeast fringe of the capital, it said.
The release of photographs apparently showing prisoners tortured and killed by the government was cited by Jarba and Western ministers. The Syrian government rejected the report as not objective and aimed at undermining negotiations.
In Damascus, where life limps on amid bombardments and checkpoints, weary residents cautiously hope for better.
"I really don't think much will come out of it, but the alternative is no talks at all, and that's not much better," said Ruba, a mother of two.