The meeting between the two rivals who faced off in the April 9-10 parliamentary election was taking place at the premier's office.
Prodi said he had requested the meeting to see if it was possible to find common ground on who will become Italy's next president.
The mandate of Italy's current president, Carlo Azeglio Ciampi, expires in mid-May. Ciampi said Wednesday he would not seek another seven-year term, possibly delaying the formation of a government by Prodi, whose center-left coalition won last month's vote by narrow margin.
It is up to president to give the mandate to form the government, and Ciampi said he would leave the task to his successor.
Ciampi, 85, cited his age and the lack of precedent for a double term in explaining his decision not to serve again, the AP reports.
A unifying and highly respected figure, Ciampi had backing from both sides and his re-election would have likely been swift. No name among those emerging as possible candidates has won backing by both sides, meaning a potentially longer process.
Berlusconi insists the president should be above the fray, and be able to reassure the country that the rights of all parties would be guaranteed. He has proposed his right-hand man, Gianni Letta, a behind-the-scenes, generally well-respected official.
The center-left is considering a few candidates for the job, including former premiers Massimo D'Alema and Giuliano Amato.
The president is elected by lawmakers of both houses of parliament and representatives of Italy's 20 regions - a total of about 1,000 officials.
The United States and NATO are conducting provocative activities both in airspace and waters of the Black Sea, Russian Defense Minister Sergei Shoygu said