The opposition said it would not meet Mr Assad's delegation unless it first agreed to sign up to a protocol calling for a transitional administration. The government rejected the demand outright and said its negotiators would return home unless serious talks began within a day.
Syrian Foreign Minister Walid al Moualem said: "If no serious work sessions are held by Saturday, the official Syrian delegation will leave Geneva due to the other side's lack of seriousness or preparedness."
Yesterday was meant to be the first time in three years of war that Mr Assad's government and foes would negotiate face-to-face.
But plans were abandoned at the last minute after the opposition said the government delegation must first sign up to a 2012 protocol, known as Geneva 1, that calls for an interim government to oversee a transition to a new political order.
Opposition delegate Haitham al Maleh said: "We have explicitly demanded a written commitment from the regime delegation to accept Geneva 1. Otherwise there will be no direct negotiations."
The government delegation met UN envoy Lakhdar Brahimi separately for less than hour and said it rejected the opposition demand.
The opposition says it has come to discuss a transition that will remove Mr Assad from power, but the government says it is there only to talk about fighting "terrorism" and that no one can force Mr Assad to go.
UN spokeswoman Alessandra Vellucci said: "There are no Syrian-Syrian talks at the moment. I cannot tell you anything about what will happen in the next few days."
Even before the announcement the direct talks had been cancelled, the outlook was dim.
One Western diplomat said: "The objective is for the first round of talks to last until next Friday, but expectations are so low we'll see how things develop day by day."
Mr Brahimi has indicated his aim is to start by seeking practical steps, like local ceasefires, prisoner releases and access for international aid deliveries, before embarking on the tougher political negotiations. But even those narrow aims would fail if the delegations go home.
Syria's civil war has already killed at least 130,000 people, driven up to one-third of the country's 22 million people from their homes and made half dependent on aid, including hundreds of thousands cut off by fighting.
Among the obstacles to progress is the position of the Islamist militants who control most rebel-held territory.
They are boycotting the talks and say anyone attending negotiations that fail to bring down Mr Assad would be traitors.
Mr Assad's main regional backer, Iran, is also not represented at the Geneva talks. UN Secretary-General Ban Ki-moon invited Tehran at the last minute but then withdrew the invitation 24 hours later when it refused to endorse the Geneva 1 protocol.
Opposition leader Ahmed Jarba said the international community had concluded Mr Assad could not stay in power.