* Three groups far apart on key issues
* Negotiations expected to run deep into the night
* Merkel needs three-way tie-up or risk losing power (Updates with compromise offer on coal-fired generation)
BERLIN, Nov 16 (Reuters) - Chancellor Angela Merkel, seeking to forge a three-way coalition or risk seeing an end to her 12-year rule, on Thursday offered bigger cuts in coal-fired power plants, but the parties remained split on immigration and other issues.
Merkel, 63, said the talks could succeed, but appealed to party leaders to "put themselves in each other's shoes" as they launched what was expected to be a long night of negotiations.
The conservative leader is trying to form an unlikely alliance with the pro-business Free Democrats (FDP) and the environmentalist Greens - a combination untested at national level - to allow her to govern for a fourth term as chancellor.
Negotiators are racing to bridge their differences on immigration, climate and finances in a marathon session on Thursday that German media are calling the "night of the long knives".
FDP deputy leader Wolfgang Kubicki suggested Merkel's self-imposed Nov. 16 deadline for concluding exploratory talks might not be met.
Merkel tried to break the logjam on climate by offering to reduce coal power generating capacity by 7 gigawatts (GW), sources familiar with the talks said. That is still shy of the 10 GW cut demanded by the Greens, but up from the earlier offer of 5 GW.
"We have very, very different positions," she told reporters earlier on Thursday. "If it works - I think it can work - there can be a positive result at the end of today's negotiations. But this is a difficult task.
"I expect the negotiations will go on for hours ... I am ready to make my contribution."
Merkel is under pressure from her own conservative bloc, in particular her Bavarian allies, the Christian Social Union (CSU), not to compromise too much to secure a coalition deal - in particular on immigration.
At stake is a conservative plan to cap the number of people Germany will accept per year on humanitarian grounds at 200,000 - a limit the environmentalist Greens reject.
"I don't know if we can resolve all the discrepancies, all the disagreements," said Joachim Herrmann, a senior member of the CSU, sister party of Merkel's Christian Democrats (CDU).
Jens Spahn, a senior CDU member, told the Passauer Neue Presse: "There won't be a coalition at any price."
JAMAICA OR BUST
Merkel is a skilled negotiator, renowned at European Union summits for building pressure on her negotiating partners and playing on their fatigue. She must leverage all these skills to secure the three-way "Jamaica" coalition, so-called because the parties' colours match those of the Caribbean country's flag.
"A failure of Jamaica would be her failure," the mass-circulation daily Bild wrote.
Merkel's partners in Germany's previous "grand coalition" were the centre-left Social Democrats (SPD), now expected to return to opposition after suffering their worst election result since 1933.
Failure to clinch a deal could lead to new elections - a scenario none of the negotiating parties wants, for fear the far-right Alternative for Germany (AfD) could make further gains after surging into parliament in the Sept. 24 national vote.
AfD co-leader Alice Weidel criticised the three-way coalition talks for failing to produce results, telling daily Die Welt: "If the (conservative) Union, FDP and Greens don't reach an agreement soon, there should be new elections."
If negotiators agree a deal after Thursday's talks, it must still pass muster with lower-ranking party officials. A key test would be a Greens conference on Nov. 25, when the party's rank and file would examine any coalition pact.
Some negotiators had little appetite to extend talks in the event of no deal overnight.
"If, after three weeks of negotiations, we can't say we can go into a stable governing alliance with each other, then three more days aren't going to help," said Annegret Kramp-Karrenbauer, CDU premier in the western state of Saarland. (Additional reporting by Riham Alkousaa, Andreas Rinke, Hans-Edzard Busemann, Gernot Heller and Andrea Shalal; Editing by Andrew Roche)