Merkel's comments come during a tense period in German-Turkish relations and amid concerns that domestic political arguments in Turkey could spill onto German streets.
Ankara was angered by the German Parliament's vote in June to label the killings of Armenians by Ottoman Turks a century ago as genocide. It also has bristled at criticism of the scope of its crackdown following a coup attempt, and complained of a lack of support from the West.
Germany is home to roughly 3 million people with Turkish roots.
"We expect of people of Turkish origin who have long lived in Germany that they develop a high degree of loyalty to our country," Merkel was quoted as telling the daily Ruhr Nachrichten.
"We try to have an open ear for their concerns and to understand them," she added, noting that the government "keeps in close contact with immigrant organizations."
On July 31, up to 40,000 people rallied in Cologne to denounce the failed coup in Turkey and show support for Turkish President Recep Tayyip Erdogan. That show of support, though it was peaceful, caused unease among some in Germany.
With two state elections due next month and a national election next year, some politicians in Merkel's conservative bloc have advocated a rethink of rules approved in 2014—at the insistence of Merkel's center-left coalition partners—that made it easier for immigrants' children to hold dual citizenship. The change largely affected Germany's Turkish community.
Merkel said that everyone who lives in Germany enjoys freedom of opinion and freedom to demonstrate, but they must deal with differences of opinion peacefully.
While her current coalition has eased rules on dual citizenship, she already has said that she won't go any further toward liberalizing them.