They say the attacker drove a 4×4 vehicle into the market in Orgun district and detonated the explosives.
The market was full of people doing their shopping for the Muslim festival Ramadan at the time of the attack.
No group has claimed the attack, but Taliban insurgents said they had not carried it out.
“We clearly announce that it was not done by the Mujahedeen of the Islamic Emirate of Afghanistan,” Taliban spokesman Zabihullah Mujahid was quoted as saying by Reuters news agency.
Eyewitnesses and medical staff said local hospitals were overrun with casualties after one of the deadliest attacks in months in Afghanistan.
The eastern province of Paktika shares a border with Pakistan’s restive and volatile tribal areas.
Orgun is one of Paktika’s safest areas, though members of the Haqqani militant network are thought to have a presence there.
Tuesday’s attack is not a surprise for security forces in the border district with Pakistan’s Waziristan region. The Pakistan-based Haqqani network is active in the area.
Last week, suicide attackers tried to assassinate local police commander Azizullah – who is widely credited with bringing security to the province, and what officials call breaking the backbone of the Haqqani network in the province.
Many car and truck bombs have been used by the Haqqani network in the province, where they have tried to target officials. But in recent years, most of the truck bombs were either defused, seized or could not reach their targets.
For the Afghan civilians, Tuesday’s attack once again brings to light how daily life is fraught with many dangers in Afghanistan. The Orgun district bazaar once a bustling town of shops and restaurants now lies in ruin, and covered in blood. The attack will continue to undermine people’s confidence in the Afghan government and the day-to-day security.
A spokesman for Afghanistan’s defence ministry told the BBC that most of the 89 bodies recovered from the rubble were women and children.
“ANA [Afghan National Army] soldiers are continuing their work of clearing rubble to look for possible survivors and victims,” Gen Zahir Azimi said.
Some 42 injured people have been taken to hospital, he added.
The district governor of Orgun District, Mohammad Raza Kharoti, earlier told the BBC that most of those killed were shopkeepers and people doing their Ramadan shopping.
One man who witnessed the attack said the blast was huge and destroyed dozens of cars and shops.
“There is no room in the hospitals for the victims, people are treating the wounded people on the streets,” he told AFP.
Eyewitnesses say police and security forces pursued the attacker before he entered the market.
One doctor at Orgun hospital, said it had become overcrowded with casualties. “We have got children, men and women injured and dead,” he said.
The attack occurred hours after two men working for the media team of outgoing President Hamid Karzai were killed by a roadside bomb in Kabul.
The Taliban said it had carried out the attack, which targeted a vehicle carrying employees of the presidential palace to work.
It comes days after Afghanistan’s two presidential candidates reached a deal to resolve a dispute over the results of last month’s presidential election.
The contenders, Abdullah Abdullah and Ashraf Ghani, agreed to accept the outcome of a vote audit after earlier allegations of voter fraud.
The dispute had revived fears for Afghanistan’s stability after the withdrawal of US-led forces later this year.