Speaking after talks in Ankara, he added there was "no space" between Turkey and the US over fighting the so-called Islamic State group -- even as his Turkish counterpart reiterated a key point of discord.
"I think the .. Longer term status of President Assad will be decided by the Syrian people," Tillerson told a joint news conference with Mevut Cavusoglu in Ankara.
Under Barack Obama's administration, the US made the departure of Assad a key policy aim, but new US President Donald Trump has put the accent firmly on defeating IS.
Ankara views the Syrian Kurdish People's Protection Units (YPG) as a "terror group" linked to Kurdish separatists waging an insurgency inside Turkey since 1984, but Washington regards them as the best force fighting the IS.
Turkey has suggested it wants to join any operation to capture the IS bastion of Raqa but without involvement of Kurdish militia.
Tillerson hailed Turkey as a "key partner" in stabilisation efforts in the fight against IS jihadists.
"There's no space between Turkey and the US and our commitment to defeat Daesh, to defeat ISIS," he added, using other names for IS.
"It is not good or realistic to work with a terror group while fighting another terror group," he added.
Years of diplomatic efforts have failed to end the Syrian conflict, which has killed more than 320,000 people and displaced millions since it started in March 2011 with protests against Assad's regime.
Tillerson met Turkish leaders Thursday for talks clouded by differences over Syria, a day after Ankara announced the end of its military offensive there.
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