Pakistan and Taliban start talks
The talks were to be originally held on Tuesday, but delayed after the government negotiators sought some clarification about the identities of the Taliban's negotiating team.
Prominent cleric Maulana Samiul Haq is leading the Taliban team.
A member of the Taliban committee and the government committee said their meeting started today in Islamabad, speaking anonymously to avoid disrupting the talks.
The meeting comes amid increasing attacks in Pakistan, and public pressure to start a military operation against the Taliban.
But, Prime Minister Nawaz Sharif says he wants to give peace another chance to end the violence.
After four hours of talks, the two sides issued a joint statement, saying both had called for avoiding any steps that could disrupt the peace process.
"It is necessary for the success of the talks that all activities against peace and security should be ended," Mr Haq told a news conference.
He said "the process of talks should not be a long one as the nation is waiting for good news. Therefore, this process should be completed in a short period."
Mr Haq also said he had asked the government negotiators to arrange a meeting between the Taliban team and the prime minister, army chief and head of the intelligence agency so that issues could be discussed with them directly.
In return, the government team also said it wanted a direct meeting with the Taliban leadership, Mr Haq said, which the cleric said he would pass on to the Taliban.
Irfan Sadiqui, the head of the government team, said there would be more talks.
"Today, we started the journey for peace, and both sides have agreed to complete it as soon as possible," he said.