Two-thirds (66 per cent) of those who responded to the ZDF Politbarometer poll said they agreed with the decision to give refuge to asylum-seekers stranded in Hungary, while only 29 per cent were opposed.
An overwhelming 85 per cent also believe that even more refugees will head to Germany, found the survey by the public broadcaster.
Berlin has said it expects to receive 800,000 asylum-seekers this year, four times as many as last year and the equivalent to about one per cent of its population.
And 43 per cent approved of Merkel's grand coalition's plans to pump an extra six billion euros into the refugee relief effort. One in four even wanted more funds unlocked, against 22 per cent who wanted the sum slashed.
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Another survey, by public broadcaster ARD Germany, showed similar sentiments, with 61 per cent saying they were not afraid that too many refugees were arriving in the country.
Despite the popular backing, the government's welcoming attitude to refugees has sparked discord within Merkel's conservative camp of CDU Christian Democrats and their CSU Bavarian allies.
"We have lost control," he said, warning that it was "completely irresponsible to allow thousands of people to enter without controlling and registering them, and one can't really estimate how many IS fighters or Islamists are among them.