"Those who work here, who are well integrated, remain welcome in Germany. That's obvious," the social-democrat leader said in a post on X, noting that "some declarations these past days have deeply destabilised our fellow citizens of Syrian origin".
Around one million Syrians live in Germany, most of whom arrived in the country during the 2015 migration crisis sparked by the civil war that broke out in Syria in 2011.
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Some have since obtained German nationality but the majority have not, making them more vulnerable to expulsion.
Germany, like other European countries including Austria and Sweden, on Monday announced they were suspending new asylum applications by Syrians -- just a day after Assad's government fell.
Later that day, Alice Weidel, the co-leader of the far-right Alternative for Germany (AfD) party, said Germany's borders "are closed, we will not accept any more".
AfD gained a huge popularity boost over the fears created by the sudden influx of migrants.
The party is tipped to finish second in February's elections, in which Weidel is aiming to claim the chancellorship.
The centre-right opposition CDU party -- currently tipped to top the polls - has also called for Syrian refugees to return home.
CDU MP Jens Spahn suggested that Berlin charter flights to Syria and offer 1,000 euros ($1,057) to "anyone who wants to return".
A German study on Friday said that the country could face labour shortages if the Syrians returned home, particularly in the healthcare industry where, according to news magazine Der Spiegel, there are 5,758 Syrian doctors working in Germany.
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