* Bavarian CSU takes hard line on migrants as state vote looms
* Merkel exploring coalition with CSU sister party, FDP, Greens
* Conservatives press for Schaeuble to quit finance ministry
* Co-leader of far-right AfD to quit party, media report
BERLIN, Sept 26 (Reuters) - Conservatives in the state of Bavaria, agonising over heavy losses in Sunday's federal election, are shaping up as a big obstacle to Chancellor Angela Merkel's bid to forge a new three-way coalition in Germany.
German voters punished Merkel's conservative bloc for her handling of the 2015 refugee crisis on Sunday, turning in droves to the far-right Alternative for Germany (AfD), which surged to third place with 12.6 percent of the vote.
Weakened, Merkel finds that her only real option of building a coalition in her fourth term is to enlist both the pro-business Free Democrats (FDP) the environmentalist Greens, who disagree on issues from energy to tax, Europe and migration.
With months of uncertainty ahead, the euro slipped to a one-month low on Tuesday after its worst day so far this year as investors worried that delays could weigh on the economy and make closer euro zone integration difficult.
Another key question for investors is whether the hawkish Wolfgang Schaeuble remains finance minister of Europe's biggest economy. On Tuesday, some conservative allies pressured him to take a new job as president, or speaker, of parliament.
While the FDP and Greens have signalled some willingness to compromise, the Bavarian Christian Social Union (CSU), which forms a parliamentary bloc with Merkel's Christian Democrats (CDU), struck a far harsher tone on Tuesday.
The prospect of lose further support to the AfD in a state election next year is making the CSU, traditionally an awkward partner, dig in its heels on its biggest concern - a cap on refugee numbers.
"The CSU has given voters guarantees and one of those is an upper limit on refugees. We must limit migration," CSU General Secretary Andreas Scheuer told the Passauer Neue Presse daily, in comments echoed by other leading figures.
Bavaria was the main entry point for migrants to Germany in 2015 and the CSU wants to limit the number of migrants to 200,000 a year.
Merkel has consistently ruled out setting a cap and the pressure on her has eased as the flow has slowed since hitting a high of nearly 1 million people in 2015. The Greens espouse a far more liberal approach and flatly repudiate limits.
"HARD BUT POSSIBLE"
Bavarian state interior minister Joachim Herrmann also reiterated the CSU's demand, but he struck a slightly more positive note about the prospects of a 'Jamaica' coalition - so-called because the parties' colours mimic the island's flag: black for CDU/CSU, yellow (FDP) and green.
"With goodwill on all sides, it is possible. But it is not easy," he told German radio.
CSU support plunged on Sunday to 6.2 percent - measured nationally - from 7.4 percent in the last election in 2013.
Many CSU lawmakers feel they are fighting for survival in the Bavarian assembly next year, where the CSU has governed for all but three years since its foundation in 1945.
The AfD, already present in 13 of Germany's 16 regional parliaments, took 12.5 percent of the Bavarian vote on Sunday, and the CSU fears its control of the Bavarian assembly could be dented just as Merkel's has been in Berlin.
Those fears are adding to the pressure on the CSU's combative leader, Horst Seehofer, who has spent much of the last two years berating the CDU for its migration policy.
"Even if Mr Seehofer said he has not 'for one second' thought about resignation, we have," said Jochen Koehler, head of a local branch of the CSU in Nuremberg that would prefer to see state finance minister Markus Soeder lead the party.
Apart from the CSU's red line on migrants, agreement with the eco-friendly Greens looks difficult on emissions policy. Bavaria is home to the luxury carmakers BMW and Audi, and the CSU is strongly resisting any prospect of bans on diesel and other combustion engines after an industry emissions scandal.
The AfD remains something of an unknown quantity, however; its co-leader and best known face, Frauke Petry, announced on Tuesday that she was quitting the party, according to German media.
Many Germans are shocked that a far-right party is entering parliament for the first time in more than half a century.
One leading AfD member has provoked outrage for saying Germans should be proud of their soldiers' achievements in World War One and Two and another for describing Berlin's Holocaust Memorial as a "monument of shame".
(Additional reporting by Andreas Rinke; Editing by Kevin Liffey)