The member of the so-called High Negotiations Committee said Kerry applied "pressure" during a weekend meeting in Saudi Arabia, warning the opposition risked "losing friends" if they failed to attend the talks.
Fuad Aliko said the Committee would meet Tuesday to make a final decision on whether to attend the Geneva talks.
The Saturday meeting with Kerry was "neither comfortable, nor positive", said Aliko, a member of the Committee's designated delegation for the talks.
"This talk means a halt to political and military support to the opposition," he added.
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Syria's warring parties were scheduled to begin the lates round of talks aimed at ending the country's conflict on Monday in Geneva.
But they have been delayed at least in part by a dispute over who will represent the opposition.
The High Negotiations Committee, a coalition of opposition bodies formed last year in Riyadh, insists it should send a sole opposition delegation to the talks.
But the Committee excludes Syria's main Kurdish force and other opposition figures, and Russia has branded some of its components as "terrorist" organisations.
But the Committee has roundly rejected either option and threatened to boycott the talks altogether if other opposition figures are included.
Aliko said Kerry applied "pressure" during the Saturday talks, though he stopped short of saying the US diplomat had used threats.
"He tried with all his efforts to insist on the necessity of us attending, saying we'd be able to do whatever we want there, but he was not able to reassure us that we are going into negotiations, rather than nothing more than a dialogue," he said.
The Geneva talks have also been held up by a dispute about some of the members of the negotiating team chosen by the Committee.
The Committee has selected Mohammed Alloush of the Islamist rebel group Army of Islam as its chief negotiator, drawing the ire of some of its other members.
Russia said last week it continues to consider the Army of Islam a "terrorist" organisation.
UN envoy Staffan de Mistura is expected to hold a press conference in Geneva later on Monday to discuss preparations for the talks.