BERLIN, Oct 1 (Reuters) - Germany"s Greens and Free Democrats met on Friday for a second round of talks to explore possiblecommon ground on which to form a new coalition government with either the Social Democrats or the conservatives, both of whom are courting them. The Greens and Free Democrats, from opposite ends of the political spectrum and at odds on a range of issues, have moved centre stage after the Social Democrats (SPD) won Sunday"s election by a narrow margin that leaves them seeking partners. Both the centre-left SPD and Chancellor Angela Merkel"s conservative bloc, which slumped to a record low result, would need the centre-right Free Democrats (FDP) and leftist Greens as partners to get a parliamentary majority for a ruling coalition. "The process began today in a good atmosphere, but has not finished," FDP leader Christian Lindner told reporters, adding that the smaller "kingmaker" parties were looking at where they could build bridges on policy issues. Lindner spoke standing next to Greens co-leaders Annalena Baerbock and Robert Habeck, who said: "We have built up a culture of conversation with each other that makes a factual discussion possible." Habeck added that the smaller parties would next each meet the larger SPD and conservatives, and "then we will see what kind of dynamic unfolds in the coming days, or perhaps weeks." Merkel, in power since 2005, plans to step down once a new government is formed and will stay on until that point. Baerbock said the Greens and FDP would keep their lips sealed about the content of their talks. After their meeting on Friday, the FDP and Greens both plan to speak separately with the larger SPD and CDU/CSU in the coming days. The Greens favour a three-way tie-up with the FDP and SPD, while the FDP would prefer the two smaller parties to join forces with Merkel"s conservatives in a "Jamaica" coalition - so-called as their colours match the island nation"s flag. "Jamaica has a chance," Markus Blume, general secretary of the Bavarian Christian Social Union (CSU), sister party to Merkel"s Christian Democratic Union (CDU), told reporters. A survey by pollster Forschungsgruppe Wahlen for broadcaster ZDF showed that 59% of respondents favoured a government alliance of SPD, Greens and FDP, with 76% saying they would like to see the Social Democrats" Olaf Scholz as the next chancellor. Asked in an interview with Spiegel magazine whether he would become chancellor after talks with the Greens and FDP, Scholz said: "Yes", adding that the partners in such a tie-up must engage with each other in a "joint government with their ideas".