"We have normalised our relations with Russia and Israel," Binali Yildirim said in a televised speech.
"Now, God willing, Turkey has taken a serious initiative to normalise relations with Egypt and Syria."
Relations between Turkey and Egypt sharply deteriorated after the Egyptian military ousted Islamist president Mohamed Morsi in 2013, a close ally of Turkish President Recep Tayyip Erdogan.
On Syria, Turkey had persistently insisted Assad's departure was key to any resolution of the country's five-year war and backed rebels trying to oust him.
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Last week, Turkey launched an operation against Islamic State jihadists and a Kurdish militia in northern Syria. Ankara said Damascus was forewarned of the operation, via Russia.
Since taking office in May, the Turkish premier has sought to resume Ankara's longstanding policy of having "zero problems" with its neighbours.
In June, Turkey mended ties with Russia which were sorely tested by the shooting down by Turkey of a Russian warplane along the Syrian border.
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