It is the first time President Recep Tayyip Erdogan has spoken publicly since his ruling AKP lost its parliamentary majority on June 7.
Speaking in the capital Ankara, the president said all sides must respect the election outcome “as the will of the people”.
The AKP is now likely to try to form a coalition, but no party has indicated it is willing to join forces with it.
Breaking his silence at a graduation ceremony for international students, Recep Tayyip Erdogan warned that history would judge anyone who left Turkey in political limbo.
Recep Tayyip Erdogan said: “We cannot leave Turkey without a government, without a head.”
He added that he hoped political parties would “prefer solution rather than crisis”.
Recep Tayyip Erdogan said he would do his part in finding a solution and that nobody should doubt he will carry out his duties within the constitution.
The AKP secured 41% of the vote in Sunday’s election, a sharp drop compared to the 2011 vote.
The party has 45 days after the final official election results are declared to form a government – but that declaration is yet to happen.
If no coalition deal is reached, a fragile minority government and early elections loom.
Earlier, PM Ahmet Davutoglu said the AKP was open to all options but warned that history had shown coalition governments were not suitable for Turkey.
“We’ve used the coalition eras of the 1970s and 1990s as an example to show that coalitions are not suitable for Turkey and we still stand by that stance,” Ahmet Davutoglu told a meeting of AKP officials.
He added that in the “current political picture” the AKP were “the only party that can come up with realistic solutions”.
Ahmet Davutoglu resigned earlier this week after the AK Party lost its parliamentary majority for the first time in 13 years, but President Recep Tayyip Erdogan asked him to stay on until a new government is formed.
Securing a working coalition will be tough, with opposition parties likely to demand limits on President Recep Tayyip Erdogan’s role.
In the build up to the election, the president had been seeking a two-thirds majority to turn Turkey into a presidential republic.
However, the pro-Kurdish People’s Democratic Party (HDP) upset Recep Tayyip Erdogan’s ambitions by crossing the 10% threshold and securing seats in parliament for the first time.
On June 11, HDP co-leader Selahattin Demirtas said his party was open to working with other opposition parties but ruled out forming a coalition with the AKP.
“Pulling Turkey into early election debates right away will not help. We believe Turkey has to continue on its way by forming a coalition,” he told reporters in Ankara.
Selahattin Demirtas also said that the jailed leader of the Kurdistan Workers Party (PKK), Abdullah Ocalan, was ready to make a call for disarmament and that a peace process with the militants should soon move forward.
He said the HDP, which has played a central role in peace talks, had visited Abdullah Ocalan on the island prison of Imrali and would be applying to make another visit soon.
The peace process with Abdullah Ocalan was launched by Recep Tayyip Erdogan in 2012 in a bid to end a three-decade conflict that has killed more than 40,000 people.
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