* 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 (Adds quotes from CSU leader Seehofer)
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) and 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 after its worst day so far this year.
Another key question for investors is whether the hawkish Wolfgang Schaeuble remains finance minister of Europe's biggest economy. 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), sounded stubborn on Tuesday.
CSU leader Horst Seehofer, for years a thorn in Merkel's side, said he had agreed with the chancellor to approach possible coalition talks "responsibly" and with a united front, but added they had to respond to voters' concerns.
"POLITICIANS MUST REACT"
CSU support plunged on Sunday to 6.2 percent - measured nationally - from 7.4 percent in the last election in 2013.
"We must make clear to the public that we understand that carrying on as we have been would not be good. The public expects politicians to react - that applies to migration and security questions and the whole social spectrum," he said.
The prospect of losing further support to the AfD in a state election next year is making the CSU, often an awkward partner, dig in its heels on its biggest concern - migrants.
"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 a limit of 200,000 migrants a year.
Merkel has consistently ruled out 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.
Many CSU lawmakers now 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.
DIFFERENCES ON DIESEL
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.
Seehofer also set out his stall on European policy, saying "strict stability" was the priority on euro zone reform, indicating a reluctance towards ideas such as a euro zone budget that could raise risks for German taxpayers.
Fears that the CSU's control of the Bavarian assembly could be dented just as Merkel's has been in Berlin have heaped pressure on the combative Seehofer. Some rivals want him to quit.
"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.
The big winner of the election may have been the AfD but it remains something of an unknown quantity. Its co-leader and best known face, Frauke Petry, said she was quitting the party, German media reported.
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".
Germany's official electoral body on Tuesday revised the conservative bloc's overall result down slightly to 32.9 percent from 33 percent, blaming a rounding error.
(Additional reporting by Andreas Rinke; Editing by Kevin Liffey)