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.
Trump was to meet Afghan President Ashraf Ghani and senior Taliban leaders on Sunday last week at his Camp David retreat after nine rounds of talks between the U.S. and Taliban representatives, held in Doha, the capital of the Gulf state of Qatar.
"The talks with the Taliban are dead", Trump said.
But throughout the negotiations, the USA -led coalition and their Afghan partners have sought to use battlefield pressure to push the Taliban into a settlement to end America's almost 18-year war.
The 18th anniversary of the September 11, 2001, terror attacks is a reminder why America can not negotiate with the Taliban, nor invite them stateside, according to Mark Levin.
Trump said if terrorists ever attack on U.S. soil again, the USA troops will go wherever they are, "and use power, the likes of which the United States has never used before".More news: Samsung Galaxy A50s, Galaxy A30s With Triple Cameras Launched in India
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A United States serviceman was killed by a Taliban vehicle bomb on Thursday, which Trump cited as the catalyst for the abrupt end to talks.
Secretary-General Antonio Guterres's Special Representative for Afghanistan, Tadamichi Yamamoto, said: "We still hear much anxiety expressed by Afghan citizens particularly in view of the Taliban's stated threat to disrupt the electoral process, especially by targeting civilians participating in the elections".
Trump's U.S. negotiator Zalmay Khalilzad had announced a peace deal "in principle" with the Taliban on Monday last.
However, the radio host said Wednesday on "The Mark Levin Show" on Westtwood One, his assertion was an expression of his own opinion and not a criticism of President Trump or any particular USA official. However Khalilzad said final approval still rested with Trump. Some 14,000 United States troops remain in the country, a fraction of the peak of about 100,000 in 2010.
A US- led invasion of Afghanistan shortly after the 2001 attack toppled the Taliban, who had harboured Osama bin Laden, the al-Qaida leader and attacks mastermind. "No enemy on earth can match the overwhelming strength, skill, and might of the American armed forces".