* Bavaria accuses chancellor of giving "totally wrong signal"

* Social Democrats, mass-circulation tabloid praise Merkel

* Coalition to discuss refugee crisis at high-level meeting

By Michael Nienaber

BERLIN, Sept 6 (Reuters) - Chancellor Angela Merkel's decision to allow thousands of migrants stranded in Hungary to enter Germany caused a rift in her conservative bloc on Sunday when her Bavarian allies accused her of giving "a totally wrong signal" to Europe.

The dispute broke out after Austria and Germany threw open their borders to thousands of exhausted migrants bussed to Hungary's border by a right-wing government overwhelmed by the sheer numbers and loath to take them in.

Germany expects a record influx of 800,000 migrants and refugees this year, by far the most in the European Union. More than 100,000 asylum seekers were registered in August alone. Europe's biggest and richest economy draws many migrants, who often have relatives already living there.

Merkel and Hungarian President Viktor Orban had agreed by telephone that the decision to let refugees -- many from Syria's civil war -- cross the borders was a temporary one made for humanitarian reasons, a German government spokesman said.

But Bavarian Interior Minister Joachim Herrmann, whose Christian Social Union (CSU) is the regional sister party of Merkel's Christian Democrats (CDU) in Berlin's ruling coalition, accused her of having pushed forward without asking Germany's federal states that had to deal with the migrant influx.

Bavarian Premier Horst Seehofer and other CSU leaders agreed in a conference call that Merkel's green light to migrants stuck in Hungary was a "wrong decision by the federal government", the mass-circulation Bild am Sonntag newspaper reported.

CSU spokesman Simon Rehak confirmed the report and said the staunchly conservative party would put the issue on the agenda of a high-level coalition meeting on Sunday evening.

But the centre-left Social Democrats, junior partner in Merkel's "grand coalition", rushed to her defence with Secretary-General Yasmin Fahimi calling her decision "the only right thing to do".

"We had to give a strong signal of humanity to show that Europe's values are valid also in difficult times. Hungary's handling of the crisis is unbearable," she said, referring to Budapest's attempts to put migrants in holding camps and a series of confrontations between Hungarian police and migrants.

Bild am Sonntag seemed to follow that argument with a headline saying: "Merkel stops the shame of Budapest".

A public opinion poll last week showed Merkel's popularity has dropped over her handling of the refugee crisis, but most Germans are not worried about the influx.

Merkel's coalition was expected to agree a series of measures later on Sunday including cutting red tape to facilitate the construction of asylum shelters, increasing funds for federal states and towns and speeding up asylum procedures.

The agenda will include widening the list of states deemed "safe" -- meaning their citizens have no claim to asylum -- probably to include Kosovo, Albania and Montenegro. Among those already deemed safe are Serbia, Macedonia and Bosnia.

With that, Berlin wants to speed up asylum and extradition procedures for migrants mainly from southeastern Europe to focus on war refugees from states like Syria, Iraq and Afghanistan. (Reporting by Michael Nienaber; Editing by Mark Heinrich)