German Chancellor Angela Merkel failed on Sunday to resolve differences within her ruling coalition on dealing with the crisis over a huge refugee influx, leaving open a row that has dented her conservatives' popularity.
Germany, Europe's biggest economy and long a magnet for migrants, expects between 800,000 and a million asylum seekers to arrive this year, twice as many as in any previous year, and far more than in any other European Union country.
The influx has opened up divisions within the coalition, with the Bavarian sister party of Merkel's conservative Christian Democrats (CDU) demanding tougher action that many in the third ruling party, the Social Democrats (SPD), oppose.
Government spokesman Steffen Seibert described talks on Sunday between the three party leaders as "constructive", but said they would meet again on Thursday. German media had billed Sunday's meeting as a crisis summit.
"There is a lot of common ground and some points that remain open and still to be settled," Steffen said, adding that these included the idea of introducing so-called "transit zones" at border crossings to process asylum requests.
Looking glum, SPD leader Sigmar Gabriel left the chancellery after a 2-hour meeting with Merkel and Horst Seehofer, leader of the Bavarian Christian Social Union (CSU).
Bavaria is bearing the brunt of the influx and Seehofer is under intense pressure from municipalities in his state to press the federal government to stem the tide of arrivals from war- and poverty-stricken areas of the Middle East, Asia and Africa.
He has issued a series of ultimatums to Merkel in recent weeks, including a threat to take the government to court over its policies on migrants, only to back down at the last minute.
Some in the CSU want to tighten or even close Germany's borders. The rhetoric became sharper than ever last week, with one senior Bavarian official saying relations between the longtime
CDU and CSU allies had reached their lowest point in nearly four decades and a German newspaper reporting Seehofer was looking into pulling CSU ministers out of Merkel's cabinet in protest.
Officials from both camps say that is unlikely.
To defuse the coalition tensions, conservative officials had expected Seehofer to come away from Sunday's meeting with a deal to introduce transit zones.
However, some SPD members have said they would not agree to the transit zones. The conservatives have had to deny that such centers would resemble concentration camps.
The infighting between the CDU and CSU conservative allies has damaged their standing. A weekly survey by pollster Emnid put support for the CDU/CSU steady at 36 percent, but still far below the 43 percent the allies enjoyed as recently as August.
Gabriel's SPD fell one percentage point to 25 percent, the poll showed. The right-wing Alternative for Germany (AfD) party gained one point to 8 percent.
Gabriel said last month that Germany must win over refugee sceptics or else risk "planting social explosives in our nation", and Germany's police chief has said the uncontrolled refugee influx poses a domestic security threat.
CDU officials say Seehofer unnerves their base with rhetoric about the refugee crisis. CSU officials counter that Merkel, who this month will celebrate her 10th anniversary as chancellor, has lost touch with voters by sticking to the open-door refugee policy she has pursued with the catch phrase: "We can do this!"