The move, days after US President Donald Trump cancelled a planned meeting with Taliban leaders at his Camp David retreat, came as the movement looks to bolster regional support, with visits also planned for China, Iran and Central Asian states.
Fawad Aman, deputy spokesman for the Afghan Defense Ministry also says three other soldiers were wounded in Thursday's attack in the Chahar Asyab district in Kabul province.
Hamza Bin Laden, a son of slain al Qaeda leader Osama Bin Laden and himself a notable figure in the militant group, was killed in a US counter-terrorism operation, the White House said on Saturday.
Police chief spokesman Abdul Ahid Walizada said on Wednesday that seven others were wounded in the Tuesday night attack in Robat Sangi district. He said an unspecified number of Taliban fighters suffered casualties.
"We're going to keep a presence there. We're reducing that presence very substantially and we're going to always have a presence.'
The foes have been meeting in Doha to finalise a deal under which the Taliban would give security guarantees in return for sharp reductions to the 13,000-strong US force in Afghanistan.
Afghanistan has been witnessing a serious escalation in violence especially targeting innocent civilians and this has to end. The capital Kabul has been rocked by back-to-back bombings
US President said he had planned a secret meeting with the Taliban's "major leaders" on Sunday at a presidential compound in Camp David, Maryland. Trump said he also planned to meet with Afghanistan's president.
Pakistan is hosting the third round of trilateral talks with Afghanistan and China to cover trade, counterterrorism and ending Afghanistan’s 18-year war.