Branding the opposition "traitors" and foreign agents, Syrian officials insisted Assad will not give up power, while the opposition said he must step down and face trial.
"After nearly three painful years of conflict and suffering in Syria, today is a day of hope," Ban said. "You have an enormous opportunity and responsiblity to render a service to the people of Syria."
Meeting for the first time since the start of the conflict in March 2011, the two sides could not be further apart at the "Geneva II" conference in Montreux on the shores of Lake Geneva.
The opposition arrived with a sole aim -- toppling Assad -- while the regime says any talk of removing the Syrian leader is a "red line" it will not cross.
"Assad will not go," Syrian Information Minister Omran al-Zohbi said on the sidelines of the conference, accusing supporters of the opposition of backing radical Islamist militants.
"If you want to support Al-Qaeda, go ahead," Zohbi said.
Syrian Foreign Minister Walid Muallem wasted no time firing a broadside at the opposition in his opening speech, which went on long beyond the allotted time of less than 10 minutes, forcing Ban to repeatedly ask him to wrap it up.
"They (the opposition) claim to represent the Syrian people. If you want to speak in the name of the Syrian people, you should not be traitors to the Syrian people, agents in the pay of enemies of the Syrian people," Muallem said.
Ahmad Jarba, the head of the opposition Syrian National Coalition, called on the regime to "immediately" sign a deal reached at the last peace conference in Geneva in 2012 setting out "the transfer of powers from Assad, including for the army and security, to a transition government."
He said that would be "the preamble to Bashar al-Assad's resignation and his trial alongside all the criminals of his regime."
Syrian state television broadcast Jarba's speech in a split screen alongside footage of death and destruction under the heading "Terrorist Crimes in Syria".
Leading a series of sharp US accusations against the Syrian regime, Secretary of State John Kerry insisted Assad cannot be part of any transitional government.
"There is no way, not possible in the imagination, that the man who has led the brutal response to his own people could regain legitimacy to govern," Kerry said.
US officials also slammed the Syrian delegation for its incendiary remarks and claims of improved aid access as "laughable."
"Instead of laying out a positive vision for the future of Syria that is diverse, inclusive and respectful of the rights of all, the Syrian regime chose inflammatory rhetoric," State Department spokeswoman Jen Psaki said.
Expectations are very low for a major breakthrough at the conference, but diplomats gathered here believe that simply bringing the two sides together for the first time is a mark of some progress and could be an important first step.
Russian Foreign Minister Sergei Lavrov warned the talks will "not be simple, they will not be quick" but urged both sides to seize a "historic opportunity".
About 40 nations and international groups were gathered, but no direct talks are expected until Friday -- when opposition and regime delegations will meet in Geneva for negotiations that officials have said could last seven to 10 days.
Erupting after the regime cracked down on protests inspired by the Arab Spring, the civil war has claimed more than 130,000 lives and forced millions from the homes.
Recent months have seen the conflict settle into a brutal stalemate -- with the death toll rising but neither side making decisive gains.
With no one ready for serious concessions, world powers will be looking for short-term deals to keep the process moving forward, including on localised ceasefires, freer humanitarian access and prisoner exchanges.
Notably absent from the table was crucial Assad backer Iran, after Ban reversed a last-minute invitation when the opposition said it would boycott if Tehran took part.
Pitting Assad's regime, dominated by the Alawite offshoot of Shiite Islam, against largely Sunni Muslim rebels, the conflict has unsettled large parts of the Middle East.
There were stark reminders of the conflict's impact in the run-up to the talks, with continued fighting on the ground and new evidence in a report alleging that Assad's forces have systematically killed and tortured 11,000 people.
At the World Economic Forum in Davos, seven major aid and human rights groups described the humanitarian crisis in Syria as the "worst of our time" and said action to alleviate suffering should not be contingent on a peace deal.
"Agreeing a negotiated peace is going to be difficult, however committing to ensuring humanitarian aid reaches all those in need shouldn't be," the groups, including Amnesty International, Care USA and Oxfam International, said in a joint appeal.