The incoming government is likely to be headed by billionaire businessman Bidzina Ivanishvili, whose Georgian Dream coalition has according to preliminary figures secured more than 80 seats in the 150-member parliament. But the talks are taking place against the backdrop of opposition claims of vote-rigging it says have denied it a more commanding majority.
Election officials said Friday that with returns from all precincts counted, Georgian Dream earned 54.9 percent of the votes cast Monday against the 40.4 percent won by Saakashvili's United National Movement.
Saakashvili will remain as the leader of Georgia until his second and last term ends in October 2013. Under a constitutional reform that goes into effect after he leaves office, many of the president's powers will be transferred to the prime minister, who is chosen by Parliament.
The new parliament will have its first sitting on Oct. 21.
Georgian Dream had hoped to gain at least 100 seats, which would be enough to enable them to make changes to the Constitution. It says violations in a number of races for individual candidates cheated it of that chance. Government officials deny that charge.
Ivanishvili indicated on the campaign trail that he would like to see the constitutional powers of the prime minister, a post he is due to occupy, expanded sooner than next October as currently envisioned.
Georgian Dream supports have picketed election body offices in a bid for results from several polling stations to be reviewed, although Ivanishvili has insisted appeals should be made through the courts.
Observers from the Organization for Security and Cooperation in Europe hailed the election overall, but had some misgivings about the vote counting process.
Despite these disagreements, negotiations appear to have gone smoothly Friday.
"We discussed the governmental transition. It was a very effective meeting," said Irakli Alasania, a member of the Georgian Dream coalition, speaking in English. "We are going to continue these discussions on Monday and we are going to have already concrete results."
By conceding defeat even before the results of the election were released, the 44-year-old Saakashvili defied the opposition's expectations that he would cling to power at all costs and preserved his legacy as a pro-Western leader who brought democracy to the former Soviet republic.
In Washington, the White House welcomed the vote as "the achievement of another milestone in Georgia's democratic development" and urged Saakashvili and Ivanishvili to "work together in the spirit of national unity."
During his nearly nine years in power, Saakashvili has pushed through economic and political reforms and attracted international investment that has led to dramatic economic growth. Poverty and unemployment, however, remain painfully high.