Turkey is already hosting at least 1.5 million refugees displaced by the Syrian conflict and has repeatedly warned that its capacities are being strained by the numbers.
Cavusoglu said supporting the rebel Free Syrian Army (FSA) was the only option for the international community against what Ankara sees as the twin threat of Islamic State jihadists and the regime of President Bashar al-Assad.
"But it has failed to achieve the desired outcome because it is fighting against both groups," he told reporters in Ankara alongside his Finnish counterpart.
Cavusoglu said there was little difference between IS militants and the Assad regime.
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"Both of them are killing people brutally and don't refrain from using any kinds of weapons at their disposal. Both force people to flee their land."
He added: "An advance on Aleppo would mean an influx of two to three million people to the Turkish border."
"And this will make Syria even more unstable. Therefore, the advance of both of them should be halted."
Turkey has repeatedly called for the ousting of Assad as the sole way to resolve the Syrian crisis permanently.
But it has grown increasingly concerned in recent months that the US-led coalition strikes against IS could end up strengthening the Assad regime.
Ankara has been seeking to persuade the United States a three-pronged approach is needed to strike against IS, Assad and Kurdish militants. But it is unclear if its arguments have made any headway with Washington.
Rebel-held areas of Aleppo are under the control of multiple groups, including fighters affiliated with the FSA.