Syria’s Foreign Minister Walid Muallem on Saturday ruled out any discussion of presidential elections.
US Secretary of State John Kerry responded by accusing Damascus of “trying to disrupt the process”.
The UN-led talks represent the first serious diplomatic intervention since Russia began air strikes in September.
At the Geneva talks, diplomats are hoping to build on the fragile and partial truce, which has reduced the level of violence in Syria since it came into effect at the end of February, notes the BBC’s Bethany Bell.
But expectations for the talks are low, she adds.
Mr Kerry met foreign ministers from France, Germany and the UK in advance on Sunday.
A cessation of hostilities agreed by most participants in the conflict began late last month. It excludes so-called Islamic State (IS) and al-Qaeda’s branch in Syria.
The purpose of the partial and temporary truce was to enable the warring sides and their foreign backers to launch a fresh attempt to end the five-year conflict.
But the latest diplomatic row began when Mr Muallem said that any talk of a new presidential election was off the agenda. “This is an exclusive right of the Syrian people,” he said.
The main Syrian opposition umbrella group, the High Negotiations Committee (HNC), said the pre-conditions could halt the talks before they had even started.
On Sunday Mr Kerry said Mr Muallem was “clearly trying to disrupt the process”, adding that Syria’s allies, Russia and Iran, had made clear “there must be a political transition and that we must have a presidential election at some time”.
French Foreign Minister Jean-Marc Ayrault said Syria’s “provocations” were a “bad sign and did not reflect the spirit of the ceasefire”.
On Sunday the HNC said it would push for an interim government in which President Bashar al-Assad and the current leadership would have no role.
The indirect talks in Geneva are mediated by the United Nations. UN special envoy to Syria Staffan de Mistura has said he wants presidential elections to be held in the next 18 months.
The fate of President Assad has been one of the main stumbling blocks in previous talks. The last round collapsed in February without agreement.
More than 250,000 Syrians have been killed and about 11 million people have been forced from their homes in five years of Syria’s civil war, which began with an uprising against Mr Assad.
Government forces, supported by Russian air strikes, have made gains against rebel fighters in recent months.
