Syria's peace conference moved into a second day Thursday with the warring sides showing no willingness to compromise as global powers seek to engineer head-to-head talks on ending the bloodshed.

The biggest push yet to end the conflict was marked by fiery exchanges on day one Wednesday as the regime and the opposition clashed over President Bashar al-Assad's fate at the UN meeting in Switzerland.

Expectations are very low for a breakthrough at the conference, but diplomats 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.

After a day of formal speeches set to be followed this week by talks involving the two sides, UN leader Ban Ki-moon urged Syria's regime and opposition to finally work together at the table.

"The world wants an urgent end to the conflict," Ban said in a closing press conference at the talks in the Swiss town of Montreux on Wednesday. "Enough is enough, the time has to come to negotiate."

But official statements made by the delegations gave no hint of compromise, as the two sides met on the shores of Lake Geneva for the first time since the conflict erupted in March 2011.

Branding the opposition "traitors" and foreign agents, Syrian officials insisted Assad would not give up power, while the opposition said he must step down and face trial.

"Assad will not go," Syrian Information Minister Omran al-Zohbi said on the sidelines of the conference.

In his speech, Syrian Foreign Minister Walid Muallem surprised observers with a vehement attack on the opposition that 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".

Damascus 'chose inflammatory rhetoric'

Jarba said that would be "the preamble to Bashar al-Assad's resignation and his trial alongside all the criminals of his regime".

Leading a series of sharp US accusations against the Syrian regime, Secretary of State John Kerry insisted Assad could not 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.

"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.

French Foreign Minister Laurent Fabius accused the regime of lowering the tone of the discussions, saying its delegation was the only one that was "deaf and blind".

"The situation is very difficult, we couldn't expect a bed of roses," Fabius said.

At his closing press conference, Kerry said Washington was also pursuing "different avenues" to resolve the conflict alongside peace talks, including "augmented support to the opposition".

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 bodies were gathered, but no direct talks are expected until possibly Friday -- when opposition and regime delegations will meet in Geneva for negotiations that officials have said could last seven to 10 days.

'Indications' sides may talk on some issues

The UN-Arab League envoy for Syria, Lakhdar Brahimi, told the closing press conference he would meet on Thursday with both sides to discuss the next step in negotiations.

"Tomorrow I am going to meet them separately and see how best we can move forward," Brahimi said.

"Do we go straight into one room and start discussing or do we talk a little bit more separately?... I don't know yet."

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 camp 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.

Brahimi said he "had indications" from both sides that they were willing discuss these issues.

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 war 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.

The opposition called at the conference for an international inquiry into the allegations.

"We have to stop this spiral of violence. We do call for an international inspection to visit places of detention and see the facts of torture that our citizens face every day," Jarba said.