Merkel was to meet President Recep Tayyip Erdogan to discuss how Turkey can help contain the historic flood of people coming from Syria, Iraq and other war zones in return for billions in aid and other European Union concessions.
Germany has been Europe's top destination for refugees, most of whom travel through Turkey and the Balkans, and expects up to one million arrivals this year -- an influx that has hurt Merkel politically.
Her poll ratings have slipped and political tensions have risen, as have attacks on asylum centres and other xenophobic hate crimes.
On Saturday, a man whom police said was motivated by “anti-foreigner sentiment" stabbed a local politician who had been active in helping migrants.
As Merkel wrestles with the biggest domestic political challenge of her career since taking office a decade ago, she was meet with Erdogan as a much-hyped EU deal with Turkey ran into difficulties.
Brussels has offered NATO member Turkey billions of euros for sheltering refugees, as well as an easing of visa restrictions, and there has been discussion about granting Turkey "safe country of origin" status.
But Erdogan has heaped scorn on Europe's efforts to deal with the crisis and urged Brussels to take Ankara's EU membership bid more seriously.
"They announce they'll take in 30,000 to 40,000 refugees and then they are nominated for the Nobel for that," he said in a jab at Merkel, who had been tipped as a Nobel Peace Prize contender for her welcoming stance to refugees.
"We are hosting 2.5 million refugees but nobody cares," he said. Merkel's visit comes a week after Turkey suffered a double suicide bombing which killed more than 100 people and a fortnight before it holds parliamentary elections, as Ankara presses a two-pronged assault on Kurdish militants and on Islamic State jihadists in neighbouring Syria.
Research institute the European Stability Initiative said although expectations were "not running high" for the crucial meeting, Berlin and Ankara "share a capacity to bring the migration crisis back under control".
"If Germany and Turkey cannot reach a deal, there are no other solutions in sight, and the mass migration of Syrians and others into the EU will continue."
- 'Racist motivation' -
More than 630,000 people fleeing war and misery in the Middle East and Africa have landed on Europe's shores this year, many making risky sea crossings from Turkey to Greece. Another 12 people drowned on Saturday off the Turkish coast, Anatolia news agency reported.
Of those who make it, most try to get to Germany, Europe's economic powerhouse, an influx that has only increased since Merkel in September made clear her country would take in people fleeing the bloody Syrian war.
While many Germans have welcomed the refugees, there has also been a backlash. Support for Merkel's conservatives dipped another point to 37 percent, a new poll said Sunday.
The long-dormant anti-Islamic PEGIDA protest movement has again drawn thousands of followers. Last week, one PEGIDA protester carried a mock gallows with Merkel's name on it.
Simmering tensions ended in violence in the western city of Cologne on Saturday when a man with a knife attacked the independent mayoral hopeful Henriette Reker, who is active in helping refugees, leaving her with serious neck wounds and injuring four others.
Police arrested the attacker who told them he had "a racist motivation" for the assault which regional police chief Wolfgang Albers described as a "political act". Investigators however said they could not rule out that the man was psychologically disturbed.
- Border fences -
As the influx continued, Hungary closed its border with Croatia, forcing the human tide to find a new more westerly route to northern Europe through Slovenia and into Austria.
Croatia on Saturday began ferrying migrants by bus and train to its northern border with Slovenia, with 3,000 crossing the frontier. Hundreds more were arriving in Slovenia on Sunday aboard a special train from Croatia.
Slovenia has said it would draft in the army to help police cope with the additional numbers.
Another 1,000 people crossed from Slovenia into Austria on Saturday and through the night, police said, with most headed for Germany, where debate continued over how to slow the influx.
Police union chief Rainer Wendt told the Welt am Sonntag newspaper Germany should build a fence along its border with Austria.
"If we close our borders this way, Austria will also close its border with Slovenia, and that's exactly the effect we need," he said, insisting that Germany could no longer send out the message that everyone was welcome.
"Our internal order is in danger, we are close to social unrest, someone has to pull the emergency brake now," he said, stressing that the only person who could do so was Merkel.