The poll released by public broadcaster ARD said Chancellor Angela Merkel's conservatives would get 32 percent of the vote, while the Social Democrats, junior partner in the ruling coalition, would get 22 percent. Together they would have 54 percent, enough for the ruling "grand coalition" to continue.
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The AfD made huge gains in two regional elections this month and will now have seats in 10 of 16 state assemblies, benefiting from a backlash against Merkel's open-door refugee policy and the arrival of nearly a million migrants last year.
The next federal election is a year from now. The party's latest score of 16 percent is more than three times the 5 percent it would need to win seats in the Bundestag or parliament for the first time.
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Founded in 2013 as a an anti-euro party, it has previously been strongest in eastern Germany, but has now broadened its appeal. It scored 14 percent of the vote in the previous ARD poll, carried out on Sept. 1.
A rueful Merkel on Monday took the blame for the regional election defeats and said she would turn back time if she could to better prepare Germany for last year's migrant influx.
The widespread backlash against her migrant policy has raised questions about whether Europe's most powerful leader will seek a fourth term next year. Given a dearth of options in her party, however, she is still the most likely candidate.
The latest ARD poll means that the AfD could become the third largest party in Germany, overtaking the pro-environment Green party on 12 percent.
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The radical Left party would capture 8 percent of the vote, while the liberal Free Democrats (FDP) would win 6 percent, allowing them to move back into parliament, the poll showed. The FDP is not currently represented in the Bundestag, but could be a potential ally for Merkel's conservatives.
The poll, conducted by Ifratest dimap for ARD, surveyed 934 people and has a margin of error of 1.4 percent to 3.1 percent.
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