The AK Party`s Culture Minister Omer Celik and Haluk Koc, the CHP`s deputy chairman and spokesman, were also present at the meeting.
"The two leaders made various evaluations in the broadest spectrum in a move not to leave the country without a government," Celik told reporters in Ankara.
"Nothing is agreed unless everything is agreed," Celik said.
He said the leaders would make a final decision on Thursday or Friday over formation of a possible AK Party-CHP coalition government.
Koc said his party`s aim was to facilitate "the formation of a coalition responsibility" which he said would contribute into "overcoming multidimensional issues".
Monday`s meeting came after the two parties ended a series of "exploratory" talks over forming a coalition that began on July 24 .
Earlier talks between the AK party and the CHP have lasted for 35 hours during five separate sessions until August 3.
In the case that the August 23 deadline expires without a government, either President Recep Tayyip Erdogan or the parliament may decide to hold a new election.
If Erdogan issues the decision, the polling is supposed to be held in the first Sunday following a 90 day period starting from the end of the first deadline.
In the current set of circumstances, this scenario suggests renewed polling in November.
However, if the parliament makes the decision for a new election, then the Supreme Election Board can reduce the 90 day period by as much as half.
The last coalition talks in Turkey were made 16 years ago, when the Democratic Left Party (DSP) of the late premier Bulent Ecevit failed to win the majority at the general election on April 18, 1999.
Since 2002, the AK Party won three general elections to continue a single-party rule for well over a decade, which ended after the June 7 elections this year produced no majority government.
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