A statement from Prime Minister Ahmet Davutoglu’s office said he had accepted their resignations and that neither would be immediately replaced, NTV channel reported.
Violence between the PKK and Turkey’s military reignited this summer after the collapse of a tentative peace process.
President Tayyip Erdogan has stepped up criticism of the pro-Kurdish Peoples’ Democratic Party (HDP) since it won 13 percent of the vote in June polls, depriving the AK Party (AKP) of an overall majority for the first time since 2002.
Earlier, the Turkish air force targeted the Kurdish rebels, killing five insurgents in the Hakkari province.
While enjoying some support among non-Kurds, the HDP is generally seen as defending Kurdish interests.
Konca and Dogan were brought into government after an inconclusive election in June, which led to the formation of a caretaker cabinet tasked with running the country until fresh elections on November 1.
While the timing of the offensive against the rebels has raised eyebrows in Turkey and overseas, the magnitude of the PKK’s response has caused widespread anger and dismay.
Speakers condemned terrorism and the violence which has rocked eastern Turkey since the resumption of fighting between the military and the Kurdistan Workers’ Party, or PKK.
His critics accuse him of using a suicide bombing in a southeastern Turkish town that was blamed on ISIL extremists as a pretext for reigniting a three-decade conflict with the PKK for electoral gain.
The HDP was the biggest victor of the June polls, taking seats from the AKP to win representation in parliament – and later in government – for the first time in the history of a pro-Kurdish party.
The Turkish opposition Republican People’s Party (CHP) had the most improvement with 28.1 percent popularity, compared to 25 percent back in June. The group, its fighters concentrated across the border in the mountains of northern Iraq, says it now seeks greater Kurdish autonomy.