At least 18 soldiers were killed in another attack on a checkpoint in West Afghanistan's Farah province.
In two other attacks on Saturday in volatile southern Helmand province, suicide auto bombs killed at least two soldiers and wounded more than a dozen others, officials said.
No group has claimed responsibility of the attack yet.
Waziri said he had no more details of the attack.
A wave of attacks across Afghanistan has left more than 25 people dead, a lot of them soldiers, officials say. A second such attack near a military base in Helmand's capital city of Lashkar Gah killed one security personnel member and wounded seven civilians.
The bombing took place in an area near an Afghan spy agency facility as well as the U.S. Embassy and other Afghan and global institutions.
Afghanistan has seen rampant instability since the 2001 invasion of the country by a United States-led North Atlantic Treaty Organisation coalition, which ousted a Taliban regime at the time.
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A Farah provincial council official Dadullah Qani told Tolo News the Taliban also captured two soldiers and stole a large amount of weapons.
Violence in Afghanistan has surged since US President Donald Trump outlined a more aggressive strategy for the country in August 2017, with US-led forces carrying out increased airstrikes and the Taliban responding with bombings, ambushes, and raids.
A suicide bomber detonated his explosives near the diplomatic area of the Afghan capital Kabul on Saturday, killing at least one person, officials said.
The Taliban, fighting to drive out foreign troops and re-establish their form of strict Islamic law, claimed responsibility.
"The Taliban can not win and their best hope for the future is to engage in reconciliation", Nicholson told reporters at a news conference in Kabul.
The official said the casualty count could rise.
The Taliban claimed the ambulance attack, as well as an attack a week earlier in which militants stormed a luxury hotel in Kabul, killing 22 people, including 14 foreigners, and setting off a 13-hour battle with security forces.