The talks were held ahead of a formal meeting tomorrow at which will the two sides are expected to discuss, among other things, the possibility of a ceasefire.
Senior journalist Irfan Siddiqui, the coordinator of the government's committee, told reporters after the talks that the response from the Taliban's political 'shura' or council to the demands of the government was "satisfactory".
The government had said earlier that talks would have to be held within the ambit of the Constitution.
In the first stage of discussions, an attempt would be made to put in place a ceasefire, he said.
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The talks were held after Jamaat-e-Islami leader Mohammad Ibrahim Khan and Jamiat Ulema-e-Islam-S spokesman Yousaf Shah returned from North Waziristan tribal region after meeting the Taliban's political shura and receiving its response to the government's demands.
The government's committee later called on Prime Minister Nawaz Sharif at his official residence. The other members of the panel are senior journalist Rahimullah Yusufzai, former ambassador Rustam Shah Mohmand and former ISI official Major (retired) Muhammad Amir.
There is intense scepticism about the initiative achieving a lasting solution to the insurgency led by the TTP, which has been blamed for hundreds of bombings and suicide attacks. Earlier in the day, 12 people were killed when three grenades were lobbed into a cinema hall in Peshawar.