Yildirim -- whose foreign minister, Mevlut Cavusoglu, made a surprise visit to Iran this week -- said Ankara will step up efforts to reduce "instability" in the region.
"We say the bloodshed needs to stop. Babies, children, innocent people should not die. That's why Turkey will be more active in trying to stop the danger getting worse in the next six months, compared with before," Yildirim told foreign reporters in Istanbul.
Yildirim said Syrian President Bashar al-Assad can remain temporarily during a transition period as "he is one of the actors today no matter whether we like it or not".
But the premier stressed that Assad has no role to play in Syria's future.
"We believe that the PKK, Daesh and Assad should not be in the future of Syria," he added, referring to the Syrian Kurds and the Islamic State group in the war-torn country.
Yildirim said it was "out of the question" for Turkey to talk with the Syrian leader, and said regional countries Turkey and Iran as well as Russia and the United States must work toward a solution in Syria.
"That is our objective. We are not pessimistic. We have even left it late. Therefore, as Turkey, we will work more because the instability there pains us."
Turkey is on the frontline of fallout from the civil war, hosting over 2.7 million Syrian refugees at a cost of $12 billion (10.6 billion euros), Ankara says.
- 'Kurds as threat'-
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After Syrian regime jets pounded US-backed Kurdish forces in northeastern Syria for a second day Friday, the Turkish premier said Damascus understood that Kurds in northern Syria have become a threat.
"This is a new situation... It is clear that the (Syrian) regime has understood the structure Kurds are trying to form in the north (of Syria) has started to become a threat for Syria too," he added, referring to the Syrian Kurds' bid to join up regions under their control.
Turkey is opposed to Syria's division along ethnic lines and the future government should not be based on an ethnic group and instead all groups including Arabs, Kurds and Alawites should be represented, Yildirim noted.
- 'Russia doesn't need Incirlik'-
Since the July 15 failed putsch, Turkey has sought to work with Iran and Russia on Syria's future and solving the crisis.
Although Russia and Iran are Assad's main allies which puts them at loggerheads with Turkey, this month Erdogan met with Russian President Vladimir Putin while Tehran's Foreign Minister Mohammad Javad Zarif came to Ankara during which Syria was on the agenda.
Turkey's foreign minister Cavusoglu even called on Moscow on August 11 to carry out joint operations against Islamic State (IS) in Syria -- and made a surprise visit to Tehran on Thursday for talks on "regional issues", according to Iranian state television.
Commenting on news reports that Russia wanted to use Incirlik air base in southern Turkey for air raids on IS jihadists in Syria, Yildirim said Moscow did not make such a demand but said "if necessary Incirlik can be used".
"I think they don't need it because they have two bases in Syria," he added, saying the news on the issue was "false".
The United States has used the Incirlik base in the southern province of Adana as a highly convenient launch pad for bombing raids against Islamic State (IS) jihadists in Syria since 2015.
Yildirim said several countries including the US were using the base "in the name of solving the problems in Syria".