* Parties appear set for talks running into weekend
* They are trying to forge untested three-way alliance
* Parties at odds on immigration, climate, finances (Releads with weekend talks, adds Merkel, Altmaier)
BERLIN, Nov 17 (Reuters) - German Chancellor Angela Merkel's efforts to forge a three-way ruling coalition look likely to drag on over over the weekend after all-night talks failed to yield a breakthrough on the divisive issues of migration and climate change.
Merkel's conservatives, the pro-business Free Democrats (FDP) and the environmentalist Greens were due to resume talks at noon (1100 GMT) on Friday, with senior figures from all three groups insisting a deal was within reach.
"I go into these negotiations with the intention, despite all the difficulties, of carrying out the task voters gave us of forming a coalition," Merkel said as she arrived for the next round. "It will be tough, but it's worth going into round two."
Her chief of staff, Peter Altmaier, told ARD television he believed the problems were "solvable," though he did not want to predict when a deal might be reached.
Failure to reach agreement could lead to new elections, something the mainstream parties fear could lead to the far-right Alternative for Germany (AfD) making further gains after surging into parliament in September.
A new election could also weigh heavily on the euro.
Merkel could still approach her previous coalition partner, the Social Democrats (SPD), but they have said they want to stay in opposition after suffering their worst election result since 1933 in the Sept. 24 poll.
A third option, a government without a parliamentary majority, would be unprecedented in Germany's post-war history.
Merkel was forced to explore the unusually tricky option of a "Jamaica coalition" - so-called because the parties' colors match the island nation's flag - after her camp lost votes to the far-right.
However the smaller parties, spanning the ideological spectrum, are under pressure from their rank-and-file supporters not to give ground as they haggle over concessions needed for a government program.
To the right, Merkel's Bavarian allies in the Christian Social Union (CSU) want a coalition accord to enshrine a hard line on immigration to shore up support in their home state, where the AfD threatens to unseat them after 60 years in power in a regional election next year.
That is anathema to the left-leaning Greens, who want to preserve the right of successful asylum seekers to bring their families to join them in Germany - a position backed by two thirds of voters, according to a poll for ZDF television.
For their part, the Greens fear giving way on their demand to shutter 10 gigawatts of polluting coal-fired power stations would alienate their voters. They have rejected Merkel's compromise offer to close 7 gigawatts.
The FDP has only just returned to parliament after four years in the wilderness and now is in no mood to compromise.
Its deputy leader, Wolfgang Kubicki, sounded the most pessimistic after the talks, telling ARD TV the parties were "still so far apart on key issues such as migration, fighting climate change, finances and domestic security, that I can't imagine how we can get together in the short time available."
The FDP wants tax cuts to please its small and medium business supporters - a tall order, given competing fiscal demands.
But a booming economy could come to parties' aid. A report by the German Chambers of Commerce and Industry on Friday found that rising tax revenues meant the government would have 76 billion euros ($89.63 billion) free to spend over four years - twice an earlier finance ministry estimate. ($1 = 0.8480 euros) (Additional reporting by Hans-Edzard Busemann, Thorsten Severin and Riham Alkousaa, writing by Thomas Escritt; Editing by Gareth Jones)