BERLIN (Reuters) - Approval ratings for German Chancellor Angela Merkel fell sharply last month, a poll showed on Friday, in the second sign of a voter backlash to her refugee policy since Islamist militant attacks in Germany last month.

With just over a year before a federal election, the poll for public broadcaster ZDF gave conservative Merkel an approval rating of 1.0, down from 1.4 in July on a scale of 5.0 to -5.0.

She came fourth in a ranking of politicians behind the Green state premier of Baden-Wuerttemberg, Winfried Kretschmann, Social Democrat Foreign Minister Frank-Walter Steinmeier and conservative Finance Minister Wolfgang Schaeuble.

The next electoral test for her conservatives comes in state elections next month in Berlin and Mecklenburg-Vorpommern that are expected to see a strong showing from the anti-immigrant Alternative for Germany (AfD).

Merkel's open-door migrant policy is under intense scrutiny after two attacks claimed by the jihadist militant group Islamic State last month.

The poll showed only 44 percent of Germans think her migrant policy is good and 52 percent view it as bad.

Although Germany has been spared Islamist attacks on the scale of those in France and Belgium, attacks on a train near Wuerzburg and at a music festival in Ansbach have shaken Germans and prompted the government to propose a range of new security measures.

The poll also showed 54 percent of Germans think the EU's disputed migrant deal with Turkey will fail. Some 35 percent believe the European Union's talks with Ankara over Turkish membership in the bloc should be stopped due to the political situation in Turkey.

Germans are worried about the integration of more than a million migrants who arrived last year alone, many fleeing war in Afghanistan, Syria and Iraq. Only two weeks ago, Merkel repeated her mantra that Germany could manage the influx of refugees and said she would not change course.

Under the refugee deal, Turkey has agreed to help stem the flow of migrants to Europe in exchange for financial aid and the promise of visa-free travel to much of the EU.

(Reporting by Madeline Chambers; Editing by Tom Heneghan)