GENEVA (Reuters) - The United Nations said on Thursday that it was extending a round of Syria talks in Geneva until Dec. 15 aimed at shaping a political solution to end the war, but that the presidency had not yet been discussed. U.N. mediator Staffan de Mistura said that the talks would focus in particular on a new constitution and U.N.-supervised parliamentary and presidential elections, as well as on 12 core principles that he declined to enumerate.  We have not discussed the issue of the presidency. We have been discussing the 12 principles. You will see they are of a broad nature but they have an impact on everything in the future constitution,  he told a news conference.  These are essential because they do refer to what could be a shared vision of the kind of Syria that the Syrians want to live in,  he said. Syria s opposition has always said that President Bashar al-Assad must step down, but his negotiators have refused to discuss the issue, and his recent successes on the battlefield have strengthened his hand.  I want to believe that that issue should come up from the Syrians through U.N.-supervised elections,  de Mistura said. With more than two weeks ahead, the round was effectively just beginning, he said, noting that the government negotiators had arrived late and might take a few days out to  consult and refresh  in Damascus before returning to Geneva around Tuesday. On Thursday he began shuttling between the two sides, installed in separate rooms off the same corridor, but he said having contact in person was less important than meeting on the substance, and the atmosphere was  professional and serious  on both sides. He said the talks had solid diplomatic backing, with recent support from Russian President Vladimir Putin, U.S. President Donald Trump, and Assad, as well as a telephone call from U.S. Secretary of State Rex Tillerson at the start of the round. The defeat of Islamic State in its main strongholds in Syria had also produced  a moment of truth .   All this takes place against quite a backdrop. It s just not a normal round of talks,  de Mistura said.   Have you seen how people are talking to each other, how those who were involved in the conflict for the first time are taking positions that are in the direction of a political dialogue?  And for the first time in eight rounds of Syria talks presided over by de Mistura, the opposition is represented by a unified negotiating team, raising the possibility of direct talks between the two sides. 