Saleh Muslim, head of the powerful Syrian Kurdish Democratic Union Party (PYD), had travelled to Geneva last week in the hopes his movement would have a seat at the table.
But he and his advisors left Geneva late yesterday, a member of his party's team in Switzerland said.
"Yes, we left Geneva because we did not get invitations," the member told AFP, speaking anonymously because he was not authorised to speak to the press.
And Ilham Ahmad, the Kurdish co-head of an Arab-Kurdish joint council in Syria, told AFP she had also left the Swiss city last night after not being invited to talks.
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The participation of Kurdish parties has been one of the sharpest points of contention among warring parties in Syria and their respective backers.
Kurdish groups like the PYD and their armed wing, the People's Protection Units, insist that their participation is key to the success of any political process aimed at ending the nearly five-year war rocking Syria.
"Without us, this process will have the same fate as the last round of Geneva talks" in 2014, the PYD source told AFP.
Russia, which has helped President Bashar al-Assad's forces regain territory since starting air strikes in late September, also says that the Kurds must take part in any talks.
But the mainstream Syrian opposition body the High Negotiations Committee -- and its Turkish and Saudi backers -- have strongly objected to the PYD's participation.