"The hospital is overwhelmed and we call on people to donate blood," said Shir Mohammad Karimi, deputy health director in Gardez, the capital of Paktia province.
A separate attack in a neighbouring province today left 15 security forces dead and 12 wounded, as militants step up their offensives following a ratcheting up in US airstrikes in a war-weary country marking 16 years of conflict this month.
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The victims of the ongoing Gardez attack, which was claimed by the Taliban in a tweet, include women, students and police, officials told AFP.
"At first a suicide bomber detonated a car filled with explosives near the training centre, making way for a number of attackers to start their assault," the interior ministry said in a statement.
A battle between the attackers, armed with guns and suicide vests, and security forces is under way inside the centre which is located near the Paktia police headquarters, it said.
Fighting has been going on for more than four hours.
A local official said two car bombs went off near the compound that also houses the provincial headquarters of the national police, border police and Afghan National Army.
"A group of gunmen have entered the compound and fighting is ongoing," Allah Mir Bahram, a member of the Paktia provincial council, told AFP.
Photos posted on Twitter purportedly show two large plumes of smoke rising above the city, suggesting two bombs were detonated in the assault.
Paktia borders Pakistan's militancy-plagued tribal areas where the Taliban-affiliated Haqqani network has a presence.
The attack came hours after a US drone strike in Pakistan's Kurram tribal district, part of which borders Paktia, killed at least 26 Haqqani militants, officials have said.
Local officials told AFP that drones were still flying above Kurram after the attack, the deadliest targeting militants in the Pakistani tribal region this year.
In Kurram last week the Pakistani military rescued a US- Canadian family who had been abducted by militants in Afghanistan in 2012. US President Donald Trump has said they were being held by the Haqqani network.
The extremist group has been blamed for carrying out spectacular attacks across Afghanistan since the US-led invasion in 2001 and is known for its frequent use of suicide bombers.
It was blamed for the truck bomb deep in the heart of the Afghan capital Kabul in May that killed around 150 people.
The Haqqanis have also been accused of assassinating top Afghan officials and holding kidnapped Westerners for ransom.
These include the recently rescued hostages Canadian Joshua Boyle, his American wife Caitlan Coleman, and their three children - all born in captivity - as well as US soldier Bowe Bergdahl, who was released in 2014.
Militants also targeted security forces in Ghazni on today, some 100 kilometres (62 miles) from Gardez, officials there said. That attack, which has ended, followed the same pattern, with "terrorists" detonating an explosives-laden Humvee vehicle near a police headquarters and attackers storming the building, Haref Noori, the Ghazni governor's spokesman, told AFP.
Fifteen security forces were killed and 12 wounded, Ghazni police chief Mohammad Zaman told AFP, adding "dozens of Taliban" also died.
The latest attacks come as four-way talks between Afghanistan, Pakistan, the United States and China were held Monday in Oman with the aim of ending the Taliban's 16-year insurgency.