The government side had asked for clarification about the Tehreek-e-Taliban Pakistan (TTP) team.
The militants have been waging an insurgency inside Pakistan since 2007.
Later, a bomb outside a hotel in a Shia neighbourhood of the north-western city of Peshawar left at least eight dead.
Twenty-six people were injured in the blast which Shafqat Malik, leader of the police Bomb Disposal Unit, said was a suicide attack.
The government and Taliban representatives had been due to start charting a “roadmap” for talks.
Many observers were puzzled by the government side’s approach. The Taliban swiftly made clear there were to be no additions to their team, and urged the government side to begin talks and see for themselves whether the team had a mandate.
Taliban negotiator Ibrahim Khan told the BBC that his side had been waiting for the talks to start throughout Tuesday and had not backed out.
“But they [the government side] have not come, so the responsibility lies on their shoulders,” he said.
“But we do not think this is an end. We are hopeful and we are here.”
Government negotiator and veteran journalist Rahimullah Yusufzai told the BBC that now certain clarifications about the composition of the Taliban team had been sorted out, his side had no objections to meeting the Taliban representatives.
“Eventually we will meet, maybe in a day or two,” he said. “But we are under no illusions that it is going to be very difficult… We are under tremendous pressure and we would like to do it away from the glare of the media.”
Prime Minister Nawaz Sharif announced the talks initiative last week, following a spate of attacks.
In January more than 100 people, including many soldiers, died in Taliban attacks across the country. Thousands have been killed in recent years.
As a result, many analysts had been expecting a large-scale military offensive against TTP strongholds in Pakistan’s tribal areas.
The BBC’s Aleem Maqbool in Islamabad says some in Pakistan worry that the talks will only allow the militants time to gain strength. Previous peace deals with the Pakistani Taliban have all failed.
As well as lead negotiator Irfan Siddiqui, Mr Sharif’s team comprises Mr Yusufzai, former ambassador Rustam Shah Mohmand and a retired major from the ISI intelligence service, Amir Shah.
Maulana Sami ul-Haq, known as the “Father of the Taliban”, was joined on the Taliban side by the chief cleric of Islamabad’s Red Mosque, Maulana Abdul Aziz and Ibrahim Khan.
The militants want Sharia (Islamic law) to be imposed throughout Pakistan and prisoners to be freed.
Former cricketer Imran Khan, a strong supporter of negotiating with the insurgents, was also asked to be part of the TTP team but declined the offer. His Tehreek-e-Insaf (PTI) party said he was not needed at the talks as another party figure, Rustam Shah Mohmand, was already on the government team.
The JUI party also turned down a fifth seat on the Taliban team.
Prime Minister Sharif, who was elected last May, has been under mounting pressure to bring the violence under control, with many accusing his government in recent months of lacking a strategy to deal with the militants.