Doha, Qatar – The head Taliban spokesman in Qatar said that the deaths of two American troops in Afghanistan overnight "should have a positive impact" on ongoing peace talks between the terrorist group and the United States by highlighting the reason the negotiations are so important: Stopping the violence.

"It is very necessary to put an end to the war," Sohail Shaheen told CBS News.

U.S.-Taliban talks have been taking place in the Gulf Arab state of Qatar, where the Taliban maintains a political office. The total number of U.S. service people to lose their lives in the Afghan conflict this year is 14. That number is already higher than all of last year.

More than 2,400 U.S. military personnel have died in Afghanistan since the war began in 2001, and though the United States formally ended its combat mission there in 2014, it still provides extensive support to the Afghan government battling the Taliban and the Islamic State of Iraq and Syria (ISIS).

The American military says the troops who were killed overnight died in a firefight, but it has not given any more details.

Deep distrust between the Taliban and the American-backed Afghan government may, however, impede the negotiations. The Taliban refuse to talk directly with Afghan government representatives, accusing President Ashraf Ghani's administration of being a puppet of the United States.

They also accuse some political leaders in Kabul of supporting ISIS, which has stepped up its attacks in Afghanistan. ISIS claimed responsibility for bombing a wedding last weekend, killing 80 people. It's an attempt, the Taliban said, to destabilize the situation on the ground and undermine any potential future Taliban role in leadership

"It is an open secret," Shaheen told CBS News. "Everyone knows about that."

Sheehan also refused to accept that al-Qaeda, the terrorist group run by Osama bin Laden, was behind the September 11th attacks.

"Still it is not known who was behind that," Shaheen insisted, despite al-Qaeda having claimed responsibility for the attacks.

"If there is proof given to us, we are ready to try (the person responsible)," he said.

Both Taliban and U.S. negotiators say they want to reach a deal to end America's longest war, but with so much distrust between the Taliban and other Afghans, charting the country's political future won't be easy.