The attack occurred on the outskirts of Ghazni city, capital of the eastern province of Ghazni, which has seen regular fighting between the Taliban and government forces.
It came as the government and Taliban are engaged in peace talks to end the war in the impoverished country that has killed tens of thousands of people in nearly two decades.
“Thirty bodies and 24 wounded people have been brought to hospital. All of them are security personnel,” Baz Mohammad Hemat, director of Ghazni hospital, told AFP.
Interior ministry spokesman Tariq Arian said a suicide bomber had detonated a vehicle full of explosives.
“The bomber drove a Humvee vehicle right inside the base and detonated it,” Ghazni governor spokesman Wahidullah Jumazada told AFP.
No group has so far claimed responsibility for the attack.
The Ghazni attack comes just days after two bombs killed 14 people in the historic city of Bamiyan, ending years of calm in the isolated town famous for its ancient Buddhist heritage.
In another suicide car bomb attack on Sunday, one civilian was killed and 20 others wounded in the southern city of Qalat in the province of Zabul, provincial police chief Hekmatullah Kochi told AFP.
He said the attack targeted the vehicle of Zabul provincial council chief, Atta Jan Haqbayan, who was wounded.
Violence surges
Sunday's bombings marked the latest carnage in Afghanistan, where violence has surged since the start of peace talks on September 12 in the Qatari capital of Doha.
Brutal attacks have killed more than 50 people in Kabul in recent weeks, including two assaults on educational centres and a rocket attack.
The three Kabul attacks were claimed by the militant Islamic State group, but Afghan officials blamed the Taliban — who denied any involvement.
The Taliban have launched daily attacks targeting Afghan forces despite engaging in the peace talks. The talks had been bogged down by disputes on the agenda, the basic framework of discussions and religious interpretations, but agreement has now been reached on all issues, according to sources close to the talks.
United States Secretary of State Mike Pompeo called for “expedited discussions” during a visit to Doha last week during which he met with both Taliban and Afghan government negotiators.
The Pentagon said earlier this month that it would soon pull out some 2,000 troops from Afghanistan, speeding up the timeline of a full withdrawal by May 2021 as agreed with the Taliban in a separate deal signed in February.
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